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$σ$ 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$

10 pages, 7 figures. Accepted for publication in MNRAS