Surely the chuck does not use the threads alone for location. Does it not have a register inboard of the threads? The register size and fit of the chuck to that register is way more important than loose or tight threads. The threads do not want to be too tight lest they try to influence the register.

DC31k is correct; the thread will be 1 3/8 x 8 and it's job is to push the chuck onto the register which IS a close fit. Colin

If you have understood my post as saying this, then I am sorry that I did not write more clearly.

A simple OD measurement of the register would give a more reliable indicator of the thread size than an OD measurement over the thread crests. If the register is 1 3/8", then it would be difficult for the thread to be 1 27/64" (27/64" is bigger than 3/8" so the register would not go over the male thread).

If the register is close to 1 27/64", then further investigation is needed, including David's metric possibility. One way may be to do a three wire measurement of the thread. There is a good online calculator somewhere for this, whose address has been posted here before. It will tell you the best size wires, but will also give you the measurement if you input the wires you are using. This means you can use three drill shanks, three drill blanks or three bits of silver steel or whatever you have to hand that is close.

On further reflection, I am wondering how a loose fit of a 1 3/8" (female?) thread leads to the supposition that the mating (male, spindle?) thread is 1 27/64", a bigger size. Surely the only way to get the two threads to mate at all is some gender reversal?