Does the F-22 (or any other stealth aircraft) carry chaff?
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.