  The frequencies of the highest-frequency kilohertz QPOs recently discovered
in some sixteen neutron stars in low-mass X-ray binary systems are most likely
the orbital frequencies of gas in Keplerian orbit around these neutron stars.
If so, these QPOs provide tight upper bounds on the masses and radii of these
neutron stars and important new constraints on the equation of state of neutron
star matter. If the frequency of a kilohertz QPO can be established as the
orbital frequency of gas at the innermost stable circular orbit, this would
confirm one of the key predictions of general relativity in the strong-gravity
regime. If the spin frequency of the neutron star can also be determined, the
frequency of the QPO would fix the mass of the neutron star for each assumed
equation of state. Here we show how to derive mass and radius bounds, using the
kilohertz QPOs, for nonrotating and slowly rotating stars, and discuss how
these bounds are affected by rapid stellar rotation and radial radiation
forces. We also describe observational results that would be strong evidence
for the presence of an innermost stable circular orbit. No such strong evidence
is present in current data, but future prospects are excellent.
