Chromaggus puts a card in your hand that costs 3 mana and buffs him or harms you. This Druid deck attempts to get control of the board, and then neutralize the hero power. It also takes advantage of the fact that Chromaggus's brood abilities place cards in your hand to fuel Twilight Drakes and early Mountain Giants.
The first five turns, he will use his green, then his red, his blue, his bronze and his black, in that order. After that, it's random. You should hold green in your hand, and always focus his board rather than his face early. Get rid of red.
I decided to hold blue, since giving up that mana on that turn put me too far behind. He will swipe your guys, possibly flamestrike, and use claw and bite to hit you in the face. He also has a spell that gives him two cards and 4 armor. You can live with it.
I'd get rid of bronze, though. He has several big dragons in his deck and his board can overwhelm you if you let him have a turn while you hold bronze.
You can get away with holding black for a turn or two, but it gives him a lot of card advantage.
He has a minion that is a 2/3 that gets +2/+2 every time you cast a spell, including using one of Chromaggus's brood powers. Kill that thing immediately. Silence it if you have to, but try to save your silences for his Twilight Drakes.
He's hard to manage early and gets easier once you can get rid of an affliction and still have enough mana to do things. Tree of Life allows you to reset your health once you stabilize, and it will also heal your giants and legendaries after they clear his board.
EDIT: FabulousUghnau in the comments suggested Lorewalker Cho, and this is an excellent idea. I pulled the second Tree of Life and replaced it with Cho, and I think it makes this deck more consistent. Brood Affliction: Green will heal you if Chromaggus is holding one, and Brood Affliction: Red will damage him. Black, Blue and Bronze only confer benefits on Chromaggus, but they will still take up space in his hand, possibly causing him to overdraw, and making it difficult for him to get any advantage out of Brood Affliction: Black.
You want to try to mulligan for Innervate or Wild Growth, to accelerate your progress to the point where you can start cleaning his afflictions out of your hand. He opens quickly, with either Claw, Faerie Dragon or an early Chromatic minion. If he plays the Chromatic guy before you can get rid of the first red affliction, it makes the game very difficult to win, and you may want to concede and try again if he does that.
If you don't have Sylvanas, Cairne or Loatheb can sub. If you don't have Foe Reaper, Ragnaros or Dr. Boom or Troggzor can also work in that slot.