We report the observation of events with fast (<=1 hr) time variability in Very Large Array observations of the Galactic superluminal source GRS 1915+105. The database consists of observations made at 67 epochs over 3 yr. We have detected fast variations on three occasions. Here we report the most remarkable of the events, observed in 1995 September 6. Over a period of approximately 2 hr, the 3.6 cm flux density of GRS 1915+105 showed several clear sinusoidal oscillations with period of 30.2 +/- 0.4 minutes, going from ~40 to ~65 mJy. We discuss possible scenarios for the production of this fast sinusoidal variation in the radio flux density and propose that the variability could be the result of a hot spot orbiting the collapsed companion of the binary system.