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We present precision radial velocity data that reveal a multiple exoplanet system orbiting the bright nearby G5V star 61 Virginis. Our 4.6 years of combined Keck/HIRES and Anglo-Australian Telescope precision radial velocities indicate the hitherto unknown presence of at least three planets orbiting this well-studied star. These planets are all on low-eccentricity orbits with periods of 4.2, 38.0, and 124.0 days, and projected masses (Msin i) of 5.1, 18.2, and 24.0 M⊕, respectively. Test integrations of systems consistent with the radial velocity data suggest that the configuration is dynamically stable. Depending on the effectiveness of tidal dissipation within the inner planet, the inner two planets may have evolved into an eccentricity fixed-point configuration in which the apsidal lines of all three planets corotate. This conjecture can be tested with additional observations. We present a 16-year time series of photometric observations of 61 Virginis, which comprise 1194 individual measurements, and indicate that it has excellent photometric stability. No significant photometric variations at the periods of the proposed planets have been detected. This new system is the first known example of a G-type Sun-like star hosting a Super-Earth mass planet. It joins HD 75732 (55 Cnc), HD 69830, GJ 581, HD 40307, and GJ 876 in a growing group of exoplanet systems that have multiple planets orbiting with periods less than an Earth-year. The ubiquity of such systems portends that space-based transit-search missions such as Kepler and CoRoT will find many multi-transiting systems.