I have discovered fast X-ray oscillations near 1000 Hz in the flux of the low-mass X-ray binary 4U 06141091 in observations with NASA’s Rossi X-Ray Timing Explorer (RXTE). Such fast oscillations in this and other X-ray binaries (see M. van der Klis et al., Proc. NATO/ASI Ser., in press [1998]) are likely produced very close to the neutron star and provide constraints on the mass and radius of the neutron star and a measurement of its spin period. The quasi-periodic oscillation (QPO) signals are observed as peaks in the power density spectra (see Fig. 1). They are usually present in pairs, the higher frequency QPO appearing between 500 and 1145 Hz with the lower frequency QPO between 480 and 800 Hz. The difference in frequency between these two signals is constant at Hz (Ford, E. C., et 323 5 4 al., 1997, ApJ, 475, L123). The existence of two QPOs with a constant frequency separation is predicted by the “beat-frequency” model. The higher frequency QPO is modulated by the spinning neutron star, producing another QPO simultaneously at lower frequency. The higher frequency QPO signal may be produced by a modulation from gas in Keplerian orbital motion in the inner accretion disk. At the highest frequencies, or smallest inner disk radii, the QPOs are produced closest to the neutron star and serve as probes of this region of strong gravitational fields. Measurements of the fastest QPO frequencies provide upper limits to the mass and radius of the neutron star, since the oscillations must originate outside the radius of the marginally stable orbit predicted by general relativity (Kaaret, P., Ford, E. C., & Chen, K., 1997, ApJ, 482, L167). The upper limits for the neutron star mass and radius in 4U 06141091 are 2.1 M, and 19 km, respectively. I have observed a robust correlation between the frequency of the QPO and the flux of a blackbody component of the Xray spectrum (Ford, E. C., et al., 1997, ApJ, 486, L47). This correlation is explained if the higher frequency QPO is associated with the Keplerian motion at an inner disk edge. An increasing mass accretion rate, reflected in an increasing blackbody flux, causes the inner disk radius to shrink. As the inner disk radius shrinks, the QPO frequency increases. From the QPO frequencies, one can measure the spin period of the neutron star in the low-mass X-ray binary, one of the observational goals of the last two decades. The beat-frequency model predicts that the neutron star spin frequency is equal to the frequency difference between the two QPOs. In 4U 06141091, the frequency separation implies a neutron star spin period of 3.1 ms.