Very-long-baseline interferometry observations have revealed a bright, compact radio component near the center of the expanding shell of supernova 1986J. The component, not present in earlier images, has an inverted radio spectrum different from that of the shell. Such an inversion has not been seen in the spectrum of any other supernova. The new component is likely radio emission associated either with accretion onto a black hole or with the nebula formed around an energetic young neutron star in the center of SN 1986J, which would directly link either a black hole or a neutron star to a modern supernova.