So I'm getting to like this as a way to cook chicken for some dinners I make, since it uses no oil. Only...when I do it, it's kinda tough.

I get boneless, skinless breasts of course. Boil enough chicken stock to cover the chicken in a pot, add chicken and veggies/spices, reduce heat and let simmer, not boil, until the chicken is done. Various recipes I saw called for anything from letting the chicken simmer 5 minutes then turning off heat entirely to letting it simmer for 30+ minutes. I stuck in a meat thermometer and cooked the chicken until it was DONE by the thermometer.

So how do you poach chicken, and is it tough when it gets done? How do I avoid that?

I have poached chicken before without it being tough. I just cook until it is done, but remember that chicken breast is generally a tougher meat than those succulent thighs.
Two other ways I cook oil free chicken:
1. The George Foreman fat buster grill. It actually cooks chicken breast, fast, oil free and tender (well tender for a breast)
2. Crock pot. The slow cooker cooks the meat so long that it goes past the tough stage to the stage where the meat doesn't even hold together. I like making shredded meats in this manner. Just put in a nice sauce for whatever else you are having (tomato base, or my hubby's fav enchilada sauce). The other nice thing about the slow cooker is you can prepare the dish the night before, store it in the fridge overnight, then pull out and set to cook all day while you are at work. Or as I am a SAHM I throw it all together after breakfast.

Somewhere on here, many moons ago, there was a recipe by a maintainer that works really well making chicken breasts for the week. She put them in a pan with the edges tucked under, and all tight together, seasoned, and baked till just done. They were tightly covered so they kind of steam cooked. Rolling the edges under kept the thinner parts from getting dried out. Using water, as in poaching, seems to pull the juice out rather than keep it moist. I guess steaming would also get you a similar result.

Well, I managed to poach them AND keep them tender!! I would've used a crock pot but my stoneware broke and I can't find a replacement. We've been putting off buying one because we're a little cash strapped with Christmas shopping going on. And we gave up on our George Foreman grill months ago. It just dried things out too much..