  We investigate the highest-frequency kHz QPOs previously detected with RXTE
in six neutron star (NS) low mass X-ray binaries. We find that the
highest-frequency kHz QPO detected in 4U 0614+09 has a 1267 Hz 3$\sigma$
confidence lower limit on its centroid frequency. This is the highest such
limit reported to date, and of direct physical interest as it can be used to
constrain QPO models and the supranuclear density equation of state (EoS). We
compare our measured frequencies to maximum orbital frequencies predicted in
full GR using models of rotating neutron stars with a number of different
modern EoS and show that these can accommodate the observed QPO frequencies.
Orbital motion constrained by NS and ISCO radii is therefore a viable
explanation of these QPOs. In the most constraining case of 4U 0614+09 we find
the NS mass must be M$<$2.1 M$_{\odot}$. From our measured QPO frequencies we
can constrain the NS radii for five of the six sources we studied to narrow
ranges ($\pm$0.1-0.7 km) different for each source and each EoS.
