We have investigated the X-ray timing properties of XTE J1550-564 during 60 RXTE PCA observations made between 1998 September 18 and November 28. We detect quasi-periodic oscillations (QPOs) near 185 Hz during four time intervals. The QPO widths (FWHM) are near 50 Hz, and the rms amplitudes are about 1% of the mean flux at 2-30 keV. This is the third Galactic black hole candidate known to exhibit a transient X-ray timing signature above 50 Hz, following the 67 Hz QPO in GRS1915+105 and the 300 Hz QPO in GRO J1655-40. However, unlike the previous cases, which appear to show stationary frequencies, the QPO frequency in XTE J1550-564 must vary by at least 10% to be consistent with observations. The occurrences and properties of the QPO were insensitive to large changes in the X-ray intensity (1.5 to 6.8 Crab). However, the QPO appearance was accompanied by changes in the energy spectrum, namely, an increase in the temperature and a decrease in the normalization of the thermal component. The QPO is also closely related to the hard X-ray power-law component of the energy spectrum since the fractional amplitude of the QPO increases with photon energy. The fast QPOs in accreting black hole binaries are thought to be effects of general relativity; however, the relevance of the specific physical models that have been proposed remains largely uncertain. Low frequency QPOs in the range 3-13 Hz were often observed. Occasionally at high luminosity the rms QPO amplitude was 15% of the flux, a level previously reached only by GRS1915+105.