Rumtscho pretty much summed it up in his comment above: You can't really stew chicken breasts (at least not from the young chickens that are found in most supermarkets). The reason is that what makes a meat "fall apart" tender is its fat and collagen content. Collagen is connective tissue that is usually found in muscles that do a lot of work for the animal. When collagen cooks in a moist environment at a low temperature for a long time (i.e., a stew), it converts into gelatin, which is soft (causing the meat to fall apart) and is interpreted by the mouth to be moist and delicious.
The problem is that the breasts don't do much work on today's factory farmed chickens. Even if you were able to find an old rooster that has lived long enough to build up some collagen, there still wouldn't be much in its breasts.
Legs and thighs, on the other hand, do have a bit more collagen and could benefit from a short stew.