We present ultraviolet and optical spectra of the first bright spot (PA = 29 degrees) on Supernova 1987A's equatorial circumstellar ring taken with the Space Telescope Imaging Spectrograph. We interpret this spot as the emission produced by radiative shocks that occur where the supernova blast wave strikes an inward protrusion of the ring. The observed line widths and intensity ratios indicate the presence of radiative shocks with velocities ranging from 100 to 250 km s^-1 entering dense (> 10^4 cm^-3) gas. These observations, and future observations of the development of the spectra and line profiles, provide a unique opportunity to study the hydrodynamics of radiative shocks. ; Comment: Accepted by ApJL on Aug. 3, 2000