We present initial observations of the newly discovered active asteroid 313P/Gibbs (formerly P/2014 S4), taken to characterize its nucleus and comet-like activity. The central object has a radius similar to 0.5 km (geometric albedo 0.05 assumed). We find no evidence for secondary nuclei and set (with qualifications) an upper limit to the radii of such objects near 20 m, assuming the same albedo. Both aperture photometry and a morphological analysis of the ejected dust show that mass-loss is continuous at rates similar to 0.2-0.4 kg s(-1), inconsistent with an impact origin. Large dust particles, with radii similar to 50-100 mu m, dominate the optical appearance. At 2.4 AU from the Sun, the surface equilibrium temperatures are too low for thermal or desiccation stresses to be responsible for the ejection of dust. No gas is spectroscopically detected (limiting the gas mass-loss rate to <1.8 kg s(-1)). However, the protracted emission of dust seen in our data and the detection of another episode of dust release near perihelion, in archival observations from 2003, are highly suggestive of an origin by the sublimation of ice. Coincidentally, the orbit of 313P/Gibbs is similar to those of several active asteroids independently suspected to be ice sublimators, including P/2012 T1, 238P/Read, and 133P/Elst-Pizarro, suggesting that ice is abundant in the outer asteroid belt.