Some folks have mentioned Beall collets that do not run true--- be sure that the problem isn't your lathe's threads before you send it back or you'll have the same issue all over again.
A fat 1" washer put onto your headstock prior to attaching the collet chuck may well solve your problem. I have a Delta and the threads on it bottom out in the Beall and the Barracuda chuck, making them run out of round. With the washer, they run dead-nuts accurate (well, for our purposes).
I have the CSA "Golden Goose" (I did not know that's what I was buying when I ordered it but I love it), a Barracuda chuck, and a Beall collet chuck.
BE SURE YOU ARE BUYING AT LEAST A 1/2" DRILL CHUCK. There are a few 3/8" chucks out there that will make you very sad if you buy them.
When you buy the collet chuck, buy it with ESPECIALLY the 1/4" collet for regular mandrels, 5/32" collets for "B" mandrels from Berea, 3/8" and 1/2" collets. These are not cheap, but worth it.
ALSO NOTE: Not all of Arizonasilhouette's closed-end mandrels will use the same collet. The Baron mandrel uses a 1/2" collet, the slimline closed-end uses something totally different (I can't remember off hand) and I wind up using the drill chuck.