Powerful radio jets from active galactic nuclei are thought to be powered by the accretion of material onto the supermassive black hole (the 'central engine')(1,2). M87 is one of the closest examples of this phenomenon, and the structure of its jet has been probed on a scale of about 100 Schwarzschild radii (R(s), the radius of the event horizon)(3). However, the location of the central black hole relative to the jet base (a bright compact radio 'core') remains elusive(4,5). Observations of other jets indicate that the central engines are located about 10(4)-10(6)R(s) upstream from the radio core(6-9). Here we report radio observations of M87 at six frequencies that allow us to achieve a positional accuracy of about 20 microarcseconds. As the jet base becomes more transparent at higher frequencies, the multifrequency position measurements of the radio core enable us to determine the upstream end of the jet. The data reveal that the central engine of M87 is located within 14-23R(s) of the radio core at 43 GHz. This implies that the site of material infall onto the black hole and the eventual origin of the jet reside in the bright compact region seen on the image at 43 GHz.