Overview
Jeskai Control with the ability to randomly win the game using Rally the Ancestors to return Kiki-Jiki, Mirror Breaker
and Restoration Angel.
Hilariously, I found this combo in a Powered Cube draft and had a blast playing it. Sure, there's no Ancestral Recall or Black Lotus in this version like there was in my draft deck, but this deck is still very strong and can be a pain to deal with. Playing out of the yard makes the deck resilient to removal, and the deck is unexpected enough that you'll likely catch a few people off guard when you use it.
Gameplan
For most of the game, you want to play a very controlling game, using the vast suite of counter-magics and removal to keep the board clear, while digging for Gifts Ungiven using all the various card filterers.
Once you have a gifts, put Kiki-Jiki and Restoration Angel into the yard, than using Rally for x equals 5 return them to the field. Kiki can then copy the resto, untapping him via blinking, then he can do it again ad nauseam. Once you have lethal on board, swing for the fences, because all the Kiki tokens have haste.
The Combo
Kiki Jiki, Mirror Breaker and Restoration Angel: As explained in the overview, Kiki and Resto are the core of the combo. Because basically all the deck does is tutor for a way to shunt these into the yard, I can afford to run one of each.
Rally the Ancestors: What returns everything back after I have found a way to bin Kiki and Resto. Kiki having haste is the glue that holds this whole thing together, because he can still do his thing once he bounces back into play. I'm running three because even more than Gifts, you need to draw this during the game or the combo just kind of dies. I don't want a full set in here, because drawing two of these just sucks.
Gifts Ungiven: Entomb is an inherently dangerous card, and this is two of them. This lets you, at Instant Speed, put both Kiki and Resto into the yard for four mana, with the added benefit of also letting you bin things for Snappy or Jace to Snap-cast. I'm running three because this is a very potent little engine in the combo, and I'm rarely unhappy to draw multiples. Note, '12/1/2004: You can choose to find fewer than four cards if you want, but your opponent will still put two of those cards into your graveyard.'
Protection
Spell Snare: There are a number of powerful two drops all across Modern, and this just says no to all of them. I chose to run two of them, because even with so many great targets, not every deck is replete with targets, and having dead cards is always bad.
Mana Leak and Remand: Two drop counter-magics are very strong, especially with Snapcaster support. I chose to run two and three because Remand draws you a card, whereas Leak only counters the spell. This might be wrong, I'm not sure.
I'm running a singleton Cryptic Command, because it is arguably the best four drop in Modern, having that much flexibility for the cost is great, but it still costs four with a colour density of three, which can be super hard to reach at times.
Filter
I'm running a pair of Jace's, because he does so much work. He gets Kiki and Resto out of my hand, he draws cards, and he snap-casts things out of the yard. His plus ability also is worth noting, and it has saved my arse a few times against decks like Zoo and Burn in playtesting.
Serum Visions: Being able to dig for combo pieces is extremely handy, and being able to draw a card for one mana can be very useful when you start to flood out. I'm running a set because it's rarely bad to draw one.
Removal
Lightning Bolt: Three damage for a paltry one mana. Bolt has defined formats since the game began. I'm running a three because there's almost no time that is bad for Bolt, and having multiples lets you kill more things. I would run four but this list is very tight and I had to make some sacrifices somewhere.
Path to Exile: Gets rid of scary things for one mana. Glistener Agent going to infekt you to death? Gone. Goblin Guide going to beat you down? Denied. Primetime ready to pound you and summon even more lands? No thanks. The drawback on this is quite intense, however. Giving someone a free land can be devastating in some matchups, so use this with a bit of caution. Because of the severity of the draw back, I chose to run only three, though you could probably sub a bolt out for one if your meta had a lot of giant scary things or a very non-basic dense mana pool.
Supreme Verdict, Day of Judgment, and Wrath of God: These vapourize all the things, which can be handy against decks that dump their hand quickly. I am running these because they have different names for Gifts fetching, and each one is powerful on its own.
Snapcaster Mage
I'm giving him his own category, because he does all the things. He's a blocker with flash, that also lets you abuse a whole tonne of the cards in the yard. He's silly with Gifts, tends to bounce back in when Rally goes off, and makes all the random little spells do stupid things. I'm running an entire set because he really is that dumb, and there's virtually no time I'd be sad to draw him, except maybe when there are no spells in my yard preventing me from casting him. He's also one of my favourite cards of all time.
Mana Base
I'll admit straight up, this needs help. I'm a tad too used to EDH, where I can run Duals and slower mana fixers, along with things that accelerate your mana in unfair ways. With that out of the way, here's my reasoning for my choices.
3 Mesa, 4 Strand, and 3 Tarn: I chose 3-4-3 Because I want to be able to get four Blue mana online first, followed by White and then Red. Strand lets me fetch my primary and secondary colours, Tarn fetches a primary and tertiary colours, and Mesa grabs my secondary and tertiary colours. I run 3-3 because even with Red being only tertiary, I really do want to be able to get one, and white is critical to combo whereas Blue isn't so much.
2 Fountain, 2 Vents, 1 Foundry: Fountain is the best land in the deck, taping for my more critical colours. Vents is OK, though I only tend to fetch it when I have a Fountain or two in play already, or if I really need to bolt something. I'm running a single Foundry, so all my Fetches can get any colour at almost any time, which is really powerful thing.
2 Prairie Stream: Testing these out. I tend to search at the end of turn, and against the decks I'm bad against like Burn and Zoo, not losing the extra life can be game changing. I also have a decent basic density, so I could potentially have these enter untapped fairly early.
3 Celestial Colonnade: Sure, it's a little slow and mana intensive, but so is a good chunk of the deck. less observant opponents might also miss you have a blocker in play and make a bad attack, though don't count on this in actual tourneys.
All the Basics: You need a decent chunk of basics, or you just fold to Blood Moon. I'm sure I have a few too many, but this traces back to my EDH playstyle, where having a decent brick of them is usually pretty good. I wanted to have at least one of each so I can fetch for them, and I added a whole tonne of Islands because in spite of not not actually being part of the combo, Blue is one colour you don't want to be unable to use.
Sideboard
Dispel: There are a number of decks that use counters in the format, and this is a solid foil to that archetype. However, it's really specific on what it counters, even more so than snare, and as such is relegated to the SB. I think two is the appropriate number, because this card's largest purpose is to win counter wars.
Elesh Norn, Iona, and Unburial Rites: While my main combo is really cute, it's bloody slow. This SB Rites package lets you deal with more aggressive plans of attack with Norn, and can also completely ruin Mono-Chrome strategies with Iona. I've stuck these as singletons, because I don't want the deck to just become 'Gifts Control.' that wasn't the point of the deck, but if this proves to just suck in every game it may begrudgingly shift to that.
Leyline of Sanctity: Burn just scoops to this, as do a few other decks. I'm only running two because there are plenty of decks this does nothing against, but damn is this a fine silver bullet.
Lightning Bolt: I really didn't want to have less than four across the seventy-five, so I relegated this one to the Sideboard for now.
Path to Exile: In matchups where the opponent plays a creature that must stick, like Infect, having a full set of these in the deck can be game winning by itself. There are enough matchups where this does practically nothing, like Tron, that running four in the main can just be wasted card slots, so I'm sticking one here.
Sword of Light and Shadow: Both of these effects are quite useful for the deck. Gaining three life buys more time to set up the combo, and returning a Jace or Snapcaster to your hand allows for some stupidity. I know it shouldn't matter, but the Foil also looks really cool.
Timely Reinforcements: There are some decks where this honestly just feels like cheating. Being Snap-cast is stupidly powerful as you'd expect it to be. The only reason it's not main is there are just so many cards I want in the main deck, and this doesn't really help the combo or protect it in a meaningful enough way to make the cut. I'm running three in the side for these reasons, and a fair number of games I add in at least two.
Wear//Tear: I'm not sure what to think of this at the moment. I saw it in a lot of SBs, so I threw a couple in, though in my admitedly limited testing I've never needed to SB them in. I may axe these from here if I never use them, but they look very good against Affinity, at the very least. Also, getting rid of Blood Moon for so little mana is something to consider.
Matchups
Burn: Burn can be a difficult matchup, because the combo takes so much bloody time to set up. The creature light variant has more spells than the deck has answers, and the creature dense version can apply too much pressure and recover too quickly for the wraths to have enough of an effect. As such, there are two different Sideboard plans for the two decks. Timely Reinforcements is the MVP pretty much every time, so it belongs in both versions. For the Spell dense one, you want to add Reinforcements, the pair of Leylines, and the two Dispels. For the Creature based one you want Elesh Norn, Reinforcements, and Unburial Rites. Sword of Light and Shadow can be good against both versions, though it is a bit slow so be wary about adding it. Pretty much the entire main combo in the deck isn't good enough here, so it can be axed completely in most cases.
Siding out (Both): -1 Kiki Jiki, -1 Restoration Angel, -3 Rally the Ancestors, -1 Island, -1 Cryptic Command
Siding in Spell Version: +2 Dispel, +2 Leyline of Sanctity, +3 Timely Reinforcements
Siding in Creature Version: +1 Elesh Norn, +1 Iona, +1 Path to Exile, +1 Unburial Rites, +3 Timely Reinforcements
Zoo: There's quite a bit of creature control built into the deck, which makes this matchup a fair bit easier than the RDW one. Spell Snare is cute but against a deck filled with 1 drops it's not worth it just to stop Tarmogoyf. Path to Exile is also not as amazing when it stops only one guy with four or five bearing down upon you. You'll want to pull in the three Timely Reinforcements so you'll almost always have some chumps, and the lifegain is very handy when your Fetches and Shocks have been dealing you damage along with their beaters
Sideboarding out for Zoo: -2 Spell Snare, -1 Path to Exile.
Sideboarding in for Zoo: +3 Timely Reinforcements.
Note, this is under construction at the moment, and when it's complete, I'd love for this to become a primer.
Thanks @PlattBonnay for the Wraths idea! Thanks @KGW for help with the Mana Base!
and Restoration Angel. 