Arthur I. Jacobs designed a great drill chuck and it has been in use for over 100 years. One of the parts inside the chuck is intentionally broken. It may be the only item you own that works and is broken at the same time.
I don't have the chuck but I don't think it would be close to fitting correctly as it would be almost 0.050" smaller than 3/4"-16. Others have speculated that the 45/64"-16 thread was requested by a machine manufacturer to fit their spindle.
Just trying to figure out where this odd thread size originated.
I suspect it is to limit its use to what it is intended for. They didn't want someone threading it onto a bolt and using the chuck to hold a chisel or punch.
I thought the thread might have been an old thread spec so I looked in my 1918 edition of Machinery's Handbook. It was not there. I suspect Jacobs used that thread so that the chuck would only thread onto what Jacobs wanted it to. In my 45 plus years machining I have seen very many special threads designed such that the threaded part would only fit what the manufacturer wanted it to fit, so no surprise at your chuck.
Eric