THE active nuclei of Seyfert 1 galaxies are characterized by a small (˜0.03 pc) region of intense broad emission lines, indicative of gas moving at extremely high velocities and ionized by a non-thermal radiation field. These spectral features are usually explained by invoking the presence of a central supermassive black hole. Here we present two-dimensional spectra of the Seyfert galaxy NGC3227, from which we have calculated the intensity maps of the emission lines, and the velocity field representing the motion of gas within the central kiloparsec of the galaxy. Surprisingly, we find that the region of broad emission lines is offset from the kinematic centre by about 250 pc, suggesting that the putative supermassive black hole is displaced from the true galactic centre. Possible explanations of this finding include the transient migration of the black hole from the galactic centre, a black hole in orbit about a central concentration of dark matter, or the capture of the black hole during the merger of NGC3227 with another galaxy.