Approximately 10% of active galactic nuclei exhibit relativistic jets, which are powered by the accretion of matter onto supermassive black holes. Although the measured width profiles of such jets on large scales agree with theories of magnetic collimation, the predicted structure on accretion disk scales at the jet launch point has not been detected. We report radio interferometry observations, at a wavelength of 1.3 millimeters, of the elliptical galaxy M87 that spatially resolve the base of the jet in this source. The derived size of 5.5 +/- 0.4 Schwarzschild radii is significantly smaller than the innermost edge of a retrograde accretion disk, suggesting that the M87 jet is powered by an accretion disk in a prograde orbit around a spinning black hole.