  We propose that some of the unidentified Galactic plane (-10 degrees < b < 10
degrees) sources listed in the first EGRET catalog (Fichtel et al. 1994) are
associated with nearby supernova remnants. The probability that the association
of strong EGRET sources with supernova remnants is due to chance alignment is
found to be < 1/2200. Three of the most convincing associations are
radio-bright, nearby shell remnants and a fourth is associated with a plerion.
  We examine possible gamma-ray production mechanisms and conclude that pion
production and decay from high-energy protons interacting with the remnant gas
could produce the gamma rays.
  The energetics of this process are in accord with theories of cosmic ray
production through supernova shock acceleration.
  The identification of pion-decay features in the gamma-ray spectra of
supernova remnants would support this interpretation.
