This seems like a straightforward enough question, but we actually have no idea whether gravity repels or attracts antimatter, all because we've never actually managed to trap enough antimatter at once to test it. That may be about to change.
The big breakthrough comes from CERN's Antihydrogen Laser Physics Apparatus (or ALPHA), who just announced that they were able to trap 309 antihydrogen atoms for 1000 seconds, or just under 17 minutes. That's an absolutely gigantic step up from the old record, which was only 38 antihydrogen atoms for just 172 milliseconds. This is finally a big enough - and, more importantly, stable enough - slab of antimatter to test just how it interacts with gravity.
The experiment itself is simple enough, as the researchers will just to need to take a decent-sized lump of antihydrogen, cool it down, and then observe how gravitational effects kick in. This has actually been tried a bunch of times before, but these earlier tests always proved inconclusive because there just wasn't enough antimatter for gravity to overcome the far stronger nuclear forces.
If all goes well, we'll know whether antimatter falls up or down by the end of the year. Personally, I'm rooting for the result that makes our universe a little bit wackier.