Jeff:

An acceptable runout for a 3-jaw is .003". To accurately measure this, you
will need to use a known standard. Something along the lines of a reamer
blank, or pin gauge, even precision ground stock (drill rod) tolerances are
+/- .003", so don't blame it all on the chuck. Further, you'll want to
ensure the jaws are clean, and the chuck is mounted on clean threads (if
it's threaded)... properly seated.

Runout in a chuck is important when you want to reposition the stock,
otherwise it's moot. Whatever you turn will be true. If you really want an
inexpensive method of re-mounting stock, then a 4-jaw independent chuck
would be a way to go. Otherwise collets would be the answer.

My $0.02