A bright, compact radio component has been discovered near the center of the expanding shell of supernova 1986J using phase-referenced VLBI imaging at three different wavelengths. The new component first appeared as an inversion in the integrated spectrum above 5 GHz. Such an inversion has not been seen in the spectrum of any other supernova. Subsequent multi-frequency VLBI measurements showed that the inversion in the spectrum is related to an unresolved component in the center of the projected shell, rather than to a known hot spot in the shell. The new component is likely radio emission associated with accretion onto a black hole or the nebula formed around an energetic young neutron star in the center of SN 1986J, which, for the first time, would directly link a black hole or a neutron star to a modern supernova.