We observed the nucleus of M33, the third-brightest galaxy in the Local Group, with the Space Telescope Imaging Spectrograph at a resolution at least a factor of 10 higher than previously obtained. Rather than the steep rise expected within the radius of gravitational influence of a supermassive black hole, the random stellar velocities showed a decrease within a parsec of the center of the galaxy. The implied upper limit on the mass of the central black hole is only 3000 solar masses, about three orders of magnitude lower than the dynamically inferred mass of any other supermassive black hole. Detecting black holes of only a few thousand solar masses is observationally challenging, but it is critical to establish how supermassive black holes relate to their host galaxies, and which mechanisms influence the formation and evolution of both.