We report the Fermi-LAT discovery of high-energy (MeV/GeV) gamma-ray emission positionally consistent with the center of the radio galaxy M87, at a source significance of over 10 sigma in ten-months of all-sky survey data. Following the detections of Cen A and Per A, this makes M87 the third radio galaxy seen with the LAT. The faint point-like gamma-ray source has a >100 MeV flux of 2.45 (+/- 0.63) x 10^-8 ph cm^-2 s^-1 (photon index = 2.26 +/- 0.13) with no significant variability detected within the LAT observation. This flux is comparable with the previous EGRET upper limit (< 2.18 x 10^-8 ph cm^-2 s^-1, 2 sigma), thus there is no evidence for a significant MeV/GeV flare on decade timescales. Contemporaneous Chandra and VLBA data indicate low activity in the unresolved X-ray and radio core relative to previous observations, suggesting M87 is in a quiescent overall level over the first year of Fermi-LAT observations. The LAT gamma-ray spectrum is modeled as synchrotron self-Compton (SSC) emission from the electron population producing the radio-to-X-ray emission in the core. The resultant SSC spectrum extrapolates smoothly from the LAT band to the historical-minimum TeV emission. Alternative models for the core and possible contributions from the kiloparsec-scale jet in M87 are considered, and can not be excluded. Show Partial Abstract