Clutch chatter is the clutch catching and releasing and catching again. The disk is probably oil soaked. Oil gets "sticky" on a clutch when it is hot, so the chatter gets worse. You will have to have the flywheel resurfaced when you do the clutch. It would also be a great time to replace the rear mounts and the pilot bearing, if need be, since you are right there.
If the clutch is oil soaked, You need to find out why, (rear main seal?,) and fix that as well.
best wishes,
Les