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ABSTRACT Fast radio bursts (FRBs) are short-duration radio pulses of cosmological origin. Among the most common sources predicted to explain this phenomenon are bright pulses from a class of extremely highly magnetized neutron stars known as magnetars. Motivated by the discovery of an FRB-like pulse from the Galactic magnetar SGR 1935+2154, we searched for similar events in Messier 82 (M82). With a star formation rate 40 times that of the Milky Way, one might expect that the implied rate of events similar to that seen from SGR 1935+2154 from M82 should be 40 times higher than that of the Milky Way. We observed M82 at 1.4 GHz with the 20-m telescope at the Green Bank Observatory for 34.8 d. While we found many candidate events, none had a signal-to-noise ratio greater than 8. We also show that there are insufficient numbers of repeating low-significance events at similar dispersion measures to constitute a statistically significant detection. From these results, we place an upper bound for the rate of radio pulses from M82 to be 30 yr−1 above a fluence limit of 8.5 Jy ms. While this is less than nine times the rate of radio bursts from magnetars in the Milky Way inferred from the previous radio detections of SGR 1935+2154, it is possible that propagation effects from interstellar scattering are currently limiting our ability to detect sources in M82. Further searches of M82 and other nearby galaxies are encouraged to probe this putative FRB population.