Recent observations of supernova remnants (SNRs) hint that they accelerate cosmic rays to energies close to ~10(15) electron volts. However, the nature of the particles that produce the emission remains ambiguous. We report observations of SNR W44 with the Fermi Large Area Telescope at energies between 2 x 10(8) electron volts and 3 x10(11) electron volts. The detection of a source with a morphology corresponding to the SNR shell implies that the emission is produced by particles accelerated there. The gamma-ray spectrum is well modeled with emission from protons and nuclei. Its steepening above approximately 10(9) electron volts provides a probe with which to study how particle acceleration responds to environmental effects such as shock propagation in dense clouds and how accelerated particles are released into interstellar space.