Chicken – Substitution for beef (veal) in a stew

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.

I'm going to assume that you are covering your meat with liquid, because if you aren't that's the problem. Collagen needs heat plus water to break down, if you don't have liquid it will turn tough as old leather.

There is no point where meat gets tougher when being slow cooked, what happens first is that the collagen breaks down, then the proteins start to denature. Generally once the collagen is all broken down is the ideal time to take it out, any longer and the meat itself starts to break down.

Things to remember:

• How long it takes for meat to get tender in a braise or slow cook method depends on the size of the cut, thickness of the cut, and the amount of collagen in it. Working cuts like chuck, rump, neck, shin, etc have lots of collagen and need a longer slow cook to break it all down. They also have more flavor. Non-working cuts like filet, sirloin, etc would need much less time, but to be honest you're wasting good money slow cooking cuts like that, roast them instead of grill them as steak! Bigger cuts and thicker cuts will need a longer slow cook as well as it takes longer for the heat and the moisture to get to the center
• Some meat will never get tender no matter how you cook them. Low-quality, poorly processed meat that has been frozen and then quick-thawed is likely to be tough as old leather no matter how lovingly you treat it in the pan. It's the GIGO principle, Garbage in-Garbage out, you can't make bad meat good with technique. So it may not be that your meat toughened up after slow cooking, it may be that it never had the potential to be tender in the first place!
• Moisture is critical with working cuts as it breaks down collagen, in a slow cooker the meat must be completely submerged in liquid. In the oven it's important to have a lid on your braising dish, or at least tin foil.