We present precision radial velocity ( RV ) data that reveal a Super-Earth mass planet and two probable additional planets orbiting the bright nearby G0V star HD 1461 . Our 12.8 years of Keck High Resolution Echelle Spectrometer precision RVs indicate the presence of a 7.4 M _ { \oplus } ~ { } planet on a 5.77-day orbit . The data also suggest , but can not yet confirm , the presence of outer planets on low-eccentricity orbits with periods of 446.1 and 5017 days , and projected masses ( M \sin { i } ~ { } ) of 27.9 and 87.1 M _ { \oplus } , respectively . Test integrations of systems consistent with the RV data suggest that the configuration is dynamically stable . We present a 12.2-year time series of photometric observations of HD 1461 , which comprise 799 individual measurements , and indicate that it has excellent long-term photometric stability . However , there are small amplitude variations with periods comparable to those of the suspected second and third signals in the RVs near 5000 and 446 days , thus casting some suspicion on those periodicities as Keplerian signals . If the 5.77-day companion has a Neptune-like composition , then its expected transit depth is of order d \sim 0.5 mmag . The geometric a priori probability of transits is \sim 8 % . Phase folding of the ground-based photometry shows no indication that transits of the 5.77-day companion are occurring , but high-precision follow-up of HD 1461 during upcoming transit phase windows will be required to definitively rule out or confirm transits . This new system joins a growing list of solar-type stars in the immediate galactic neighborhood that are accompanied by at least one Neptune ( or lower ) mass planets having orbital periods of 50 days or less .