OF COURSE there is carryover from pulldowns to pullups or chinups. It is using the same muscle groups in a very similar way.
I agree with Gummi-Hulk above. 3 sets of 8-10 reps, moving up in weight when you can get 3 sets of 10 should be helpful. Make sure to get full range of motion, especially at the top, as that simulates the bottom of a chin, which is often the toughest part.
KSC recommended 3-5 sets of 8-12 reps, and that seems to be consistent with some of the responses here. This works out since I did 3x10 today. Was pretty much at failure on the last rep.