We have observed a 3° × 3° area centered on the M81/M82 group of galaxies using the Robert C. Byrd Green Bank Telescope in a search for analogs to the high-velocity clouds of neutral hydrogen found around our Galaxy. The velocity range from –605 to –85 km s–1 and from 25 to 1970 km s–1 was searched for H I clouds. Over the inner 2° × 2° the 7σ detection threshold was 9.6 × 105 M sun. We detect five previously unknown H I clouds associated with the group, as well as numerous associated filamentary H I structures, all lying in the range –105 ≤ V helio ≤ +280 km s–1. From the small angular distance of the clouds to group members, and the small velocity difference between group members and clouds, we conclude that the clouds are most likely relics of ongoing interactions between galaxies in the group.