Most any 3 jaw chuck can, and often does, have runout at some point of gripping. Like the others above, 0.003 is not too bad. Not perfect, but not bad. In all of history, there's only been one perfect man, and they've been putting erasers on pencils ever since. Even high end chucks can have runout, for several reasons. A practice you might find useful, if there isn't time to properly run down the real problem, is to determine which sequence of jaws is closest to true center, This is a very real problem, and the older the chuck, the more noticable the misalignment is.
The first time you do this, it sounds complicated. The second time is quite easy, and the third you wonder "why I didn't think of this myself". Remove the jaws, set them in sequence, and mark them 1-3 with a file or grinder. The jaws are usually hardened, a punch mark won't cut it. Number one(1) will be with the teeth closest to the gripping end. Looking into the slots you will find the "scroll" that moves the jaws. Brush any chips out, a tooth brush works well here. It will take several rotations of the scroll to get things reasonably clean. Cleaning the chuck scroll can be with the chuck body on the bench. The chuck must be mounted to test runout. Be sure the spindle threads are clean as well.
Rotate the scroll to where it is almost but not quite in a slot. Insert the Nr 1 jaw here, marking it with a sharpie or some other erasable mark. proceeding to Nr 2 and 3 as the scroll is rotated. Chuck up a test bar and record runout. Remove the chuck jaws and start Nr 1 jaw in the Nr 2 slot, repeating the tests. Then with the Nr 1 jaw in the Nr 3 slot, again repeating. This test could be repeated several times, depending on how well the test bar is chucked.
With the tests complete, determine where the lowest runout is. Mark that slot with a punch as Nr 1. The chuck body is softer than the jaws so a punch mark will work. Mark slot 2 and 3 as well. Also put a witness mark for the chuck body and the backing plate. That way when the chuck is disassembled for cleaning, which should happen regularly, it can be reassembled as it came apart. Follow this with the "outside" jaws, marking the jaws with a sharpie until they are registered. Then with a grinder or file.
This test defines the "lay" of the chuck. I don't know the proper machinist's term for the process. When the chuck is assembled by the manufacturer, this test is usually not a part of the assembly process. Further, the chuck likely hasn't been properly cleaned, All of this can effect the accuracy of runout. A HF machine, and many others, seldom come from the supplier "ready to run". Some tune up is as important as gaining the "feel" for a particular machine.
My terminology is learned from very old (>100 yo) books, long before the Internet was a "thing". The terms used may be "incorrect" by modern usage. This is the sequence I followed with a Grizzly model made in Taiwan. The recent version is G-4000, made in Mainland China. The brother to your HF machine. I use a Dremel with a cut-off wheel to mark the jaws.
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