We report the first observation of gravity wave momentum flux in the mesosphere using the dual-beam Arecibo incoherent scatter radar (ISR). Quasi-monochromatic waves were observed throughout the daytime of July 28, 2001 in the altitude range of 65--85 km. The largest wave speed was about 100 m/s and the dominant period was about 15 min. Instability, as indicated by the Richardson number, occurred at several altitudes, most dramatically at 77 and 81 kilometers. The zonal momentum flux is found to change sign at altitudes where dynamical instability occurs. No significant gravity waves were observed in the region having an eastward background wind, while they were ubiquitous when the background wind was westward.