Did you surface the flywheel?
Did you get any grease or oil on the clutch friction surfaces (did you wash your hands)?
Did you clean the flywheel and pressure plate with brakleen or the like?
How are your engine mounts?
Do you have an oil leak that may have contaminated the new clutch?
These are the most common causes of chatter.
86 Corvette Coupe
94 Corvette Coupe
Old K30 GMC