If you made sure everything was clean before fitting the chuck to the spindle and you find run-out after that check the inside bore where the collet fits for runout, if that's as good as the spindle then the problem is with the collets.
For what you paid you really can't expect anything too good in the way of accuracy, a half decent chuck would cost as much as your total purchase, you don't say what type of collets but a good ER25 collet will set you back around £15, even more if you want greater accuracy but that is a waste of money if the chuck has any runout.

You may be able to return the collets and/or the lot for a refund.

Emgee

What are you using to measure, a DTI

Don’t use a dti – use a dial gauge. One only indicates a change, the other actually measures the change.

Bill, Not done it yet is being a little precise and could be more helpful if he had explained the difference. I believe that a DTI is a finger gauge which Generally has a smaller movement that a Dial Gauge. That said, all the DTIs that I have seen are graduated and equally acceptable for measuring distance within their range.

For John's application, I would consider a DTI or Dial Gauge to be quite acceptable.

Bob

Hi John, Guys,

Check the insides of your collets very carefully !

This is what most of mine were like. I used a Stanley knife blade and a stone to clean the swarf remains up. After that I could easily get a couple of tenths of a thou or better.