Where in Houston are you located? I live on the West side of town, about a mile north of I-10 and 1/4 mile SE of the intersection of BW8 and Hammerly Blvd.
I am afraid that your only viable solution if the problem is actually the chuck is going to be to return it to Shars. Mikey is correct that you can't normally expect to get 0.000" runout with a solid-body 3-Jaw chuck. But if they advertise 0.003 Max, then 0.014" is definitely excessive. But first there are some more checks that you should make.
First, confirm that each jaw is in its correct slot. Both the slots and the jaws should be numbered from 1 to 3.
Then set up a dial indicator and measure the runout of the spindle register. While you are at it, measure the runout of the 3MT taper, although that has nothing to do with the chuck runout.
Mount a dog driver plate (often incorrectly called a drive plate) on the spindle. Mount a dead center in the spindle and a live center in the tailstock ram. Install a dog on a precision test bar and mount the bar between centers. Check its runout at three or four places and if not 0.000" rotate it relative to the spindle and adjust for minimum. Match-mark spindle or drive plate and bar. Then either video tape it or photograph it. Remove the back plate from the chuck, dismount the test bar, and mount it in the chuck. Finally, re-mount the bar and chuck between centers and indicate the register area on the rear of the chuck. Assuming that the bar has no runout and the back plate was perfectly made, you should get 0.014" runout on the chuck register. Photograph this for the record and send the chuck and the photographs all back to Shars.
I would suggest that you spend the extra bucks and buy a Buck-style chuck with 2-piece jaws.