OSSE observed the starburst galaxy M82 in two viewing periods of 8 and 14 days. M82's priority as a target had been established on the grounds that the average supernova rate may be very high there, so that a significant chance of 56 Co detection exists. If M82 is at 3.4 Mpc distance, normal Type II (e.g. SN1987A) are too dim in 56 Co lines, but the Wolf-Rayet derived Type Ib, which are also massive-star core implosion objects, might be detectable to OSSE. 1,2 Expected fluxes of the 847 keV γ-line of 56 Co would be near (2-5)× 10 -5 γ cm -2 s -1 . A Type Ia in M82 would be very bright,3 near (3-6) γ 10 -4 -γ cm -2 s -1 . We present OSSE background subtracted spectra of the M82 region for viewing periods 7 and 18. These spectra show no significant excess at 847 keV or at 1238 keV, the two strongest 56 Co γ-lines. When we fit a smooth gamma continuum plus a feature having both the 847 keV and 1238 keV lines to the OSSE data, we obtain for the 847 keV line amplitude the values (-4.18 ± 3.45) × 10 -5 -γ cm -2 s -1 for viewing period 7 and (0.84 ± 2.85) × 10 -5 γ cm -2 s -1 for viewing period 18. We discuss the implications on the supernova rate in M82.