We report the discovery of 47 low surface brightness objects in deep images of a 3 \arcdeg \times { } 3 \arcdeg field centered on the Coma cluster , obtained with the Dragonfly Telephoto Array . The objects have central surface brightness \mu ( g, 0 ) ranging from 24 – 26 mag arcsec ^ { -2 } and effective radii r _ { eff } = 3 \arcsec – 10 \arcsec , as measured from archival Canada France Hawaii Telescope images . From their spatial distribution we infer that most or all of the objects are galaxies in the Coma cluster . This relatively large distance is surprising as it implies that the galaxies are very large : with r _ { eff } = 1.5 kpc – 4.6 kpc their sizes are similar to those of L _ { * } galaxies even though their median stellar mass is only \sim 6 \times 10 ^ { 7 } M _ { \odot } . The galaxies are relatively red and round , with \langle g - i \rangle = 0.8 and \langle b / a \rangle = 0.74 . One of the 47 galaxies is fortuitously covered by a deep Hubble Space Telescope ACS observation . The ACS imaging shows a large spheroidal object with a central surface brightness \mu _ { 475 } = 25.8 mag arcsec ^ { -2 } , a Sersic index n = 0.6 , and an effective radius of 7 ^ { \prime \prime } , corresponding to 3.4 kpc at the distance of Coma . The galaxy is not resolved into stars , consistent with expectations for a Coma cluster object . We speculate that these ‘ ‘ ultra-diffuse galaxies ’ ’ ( UDGs ) may have lost their gas supply at early times , possibly resulting in very high dark matter fractions .