We report the discovery of high-energy (E>100 MeV) gamma-ray emission from NGC 1275, a giant elliptical galaxy lying at the center of the Perseus cluster of galaxies, based on observations made with the Large Area Telescope (LAT) of the Fermi Gamma ray Space Telescope. The positional center of the gamma-ray source is only ~3 away from the NGC 1275 nucleus, well within the 95% LAT error circle of ~5.The spatial distribution of gamma-ray photons is consistent with a point source. The average flux and power-law photon index measured with the LAT from 2008 August 4 to 2008 December 5 are F_gamma = (2.10+-0.23)x 10^{-7} ph (>100 MeV) cm^{-2} s^{-1} and Gamma = 2.17+-0.05, respectively. The measurements are statistically consistent with constant flux during the four-month LAT observing period.Previous EGRET observations gave an upper limit of F_gamma < 3.72x 10 ^{-8} ph (>100 MeV) cm^{-2} s^{-1} to the gamma-ray flux from NGC 1275. This indicates that the source is variable on timescales of years to decades, and therefore restricts the fraction of emission that can be produced in extended regions of the galaxy cluster. Contemporaneous and historical radio observations are also reported. The broadband spectrum of NGC 1275 is modeled with a simple one-zone synchrotron/synchrotron self-Compton model and a model with a decelerating jet flow.
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