  We discuss the case for using the Next Generation Very Large Array both to
discover new black hole X-ray binaries astrometrically, and to characterize
them. We anticipate that the ngVLA will be able to find $\sim$100 new black
hole X-ray binaries, as well as a host of other interesting radio stars, in a
few hundred hour survey. Parallax and astrometric wobble measurements will be
achievable in feasible follow-up surveys especially using long baseline
capabilities. The ngVLA's high angular resolution, high survey speed, and high
frequency sensitivity give it a unique range of parameter space over which it
is sensitive.
