Absolutely ! Cut the meat into about 1" cubes. Chill in the freezer for about 1/2 an hour. You don't want it hard, just firm and really cold. Do not just turn it on and let it rip. This is the time for the "pulse" "pulse" "pulse" action. Say "one alligator" for each pulse (that's approximately one second). If you can't get all the meat done in one batch, empty the bowl and repeat. I've never found the need for liquid, in fact, I'd think that would lead to more possibility of a puree/mousse type texture than ground meat. I do this all the time when I can't find ground pork/chicken/veal/turkey at the market.

You should be fine, I use mine all the time to make ground beef or lamb. A few tips though - cube your chicken and then put it in the freezer for 15 minutes or so, you don't want it frozen, just firm-ish. Then put a cup or some of cubed chicken in the processor and pulse, a second at a time, until it's chopped-ish. Take that chicken out and repeat with more chicken.

Cold meat + not too much + quick pulses = ground meat
warm meat + too much + long grind time = meat puree

I also recommend the grinder attachment for Kitchen aid mixers, if you have one. It works quite well and makes grinding meat super-duper easy.

Start with about 1/2 cup of liquid like chicken broth. Then add a coupe of cups of cubed chicken and give it a whirl. If the motor seems to bog down significantly. Remove a quarter of the chicken and try again. It will probably mince chicken but may not be able to handle larger quantities.

Now if it does fine with 2 cups of cubed chicken you could try three cups then next batch. And from that test, then you can make a decision about how much more it can handle.