Using the Position Sensitive Proportional Counter on ROSAT, we detected soft X-ray emission from SN 1986J in NGC 891 approximately 9 years after the supernova event. The X-ray emission is characterized by L(x) (0.1-2.5 keV) = 1.6-7 x 10(40) ergs s-1, T(x) = 1.0-3.9 keV, and an absorbing column of 5-14 x 10(21) cm-2. The X-ray luminosity, temperature, and absorption column are reproduced surprisingly well in a model where a reverse shock propagates into the outer layers of the exploded star. The large absorbing column is probably intrinsic to the supernova and represents the cooled gas created by a radiative reverse shock.