We report on the discovery of cool gas inflow toward six star-forming galaxies with redshifts z \sim 0.35 - 1 . Analysis of Mg ii and Fe ii resonance-line absorption in Keck/LRIS spectroscopy of this sample reveals velocity shifts of 80 - 200 { km s ^ { -1 } } and equivalent widths for inflowing gas of \gtrsim 0.6 Å in five of the six objects . The host galaxies exhibit a wide range in star formation rates ( SFR \sim 1 - 40 ~ { } M _ { \odot } ~ { } \mathrm { yr } ^ { -1 } ) and have stellar masses similar to that of the Milky Way ( \log M _ { * } / M _ { \odot } \sim 9.6 - 10.5 ) . Imaging from the Hubble Space Telescope Advanced Camera for Surveys indicates that five of the six galaxies have highly inclined ( i > 55 ^ { \circ } ) , disk-like morphologies . These data represent the first unambiguous detection of inflow into isolated , star-forming galaxies in the distant universe . We suggest that the inflow is due to the infall of enriched material from dwarf satellites and/or a galactic fountain within the galaxies . Assuming that the material has been enriched to 0.1 Z _ { \odot } and has a physical extent approximately equal to that of the galaxies , we infer mass inflow rates of dM _ { \mathrm { in } } / dt \gtrsim 0.2 - 3 ~ { } M _ { \odot } ~ { } \mathrm { yr } ^ { -1 } for four of these systems . Finally , from comparison of these absorption lines to the profiles of Mg ii and Fe ii absorption in a larger spectroscopic sample of \sim 100 objects , we measure a covering fraction of cool inflow of at least 6 \% , but can not rule out the presence of enriched infall onto as many as \sim 40 of these galaxies .