Considering it is nearly undetectable on radar, it seems like it wouldn't have to worry about radar guided missiles; in addition to this it is sure to have sophisticated jamming capabilities. So why carry chaff? Just weight.
It certainly seems so.
Stealth aircraft are not invisible to radar, only less visible. Under certain conditions the adversary will be able to get a radar lock:
- At close distance
- With very high (focused) radar energy
- At certain angles of incidence
Given these risks and the low weight of chaff, it wouldn't be be wise to not carry it.
One source that claims the F-22 carries chaff: http://science.howstuffworks.com/f-22-raptor8.htm
It releases flares to confuse heat seekers and sends out chaff, small pieces of reflective material, to disperse radar waves and confuse a radar-guided missile's tracking system.
It's even been used in the field, according to The Washington Post:
the [F-22s] shot flares and even chaff — clouds of metal meant to confuse radar systems but possibly used in this case as an additional visual warning.