Fat in chicken skin after boiling
Yes, it depends on how long you cook the chicken.  Much of the fat is in the skin and can be removed by peeling it; other fat (such as in the thighs) tends to stick around.  Long, slow cooking will render more of the fat, which melts at around 95° F.

I'm guessing you're trying to avoid fat for dietary reasons, but consider saving it for future cooking purposes - like where you might use another oil.  It's delicious, and not terribly harmful in small quantities.