Thanks all, for your replies. I knew I was presenting a general
symptom with lots of potential culprits. I should've been a little
more specific in my original message. But now I have an extensive
checklist to work through. Let me push my luck and throw a few more
questions at you. First some specifics.

Chatters came about after:
removing failed 2.1 waterboxer engine with transmission attached
separating transmission from failed engine
swapping clutch et al (year old) to rebuilt engine from AVP (came
with reconditioned flywheel)
installing rebuild after attaching transmission
replaced one badly worn motor mount in the process

Since fumbling blindly through the installation of the rebuild, I
suspect grime/oil as the cause of the chatters. I was up to my ears
in the stuff for longer than I would like to admit  so it is likely
that some made it on to the pressure plate. Yikes. Will it dissipate?

I foolishly only replaced one motor mount that was particularly bad
and am wondering if its rigidity  next to the older mounts might be a
culprit. Is it standard procedure to replace all mounts at once? What
about alignment of transmission to engine? I didn't use a centering
tool but had little trouble pulling the two together. Engine and
transmission went in easily as well.

Don't want to get into the throwing parts game, so I guess I'll start
by tightening all mounts...

Thanks again for the help.
Chase