We present observations of Q1549-C25, an ~L* star-forming galaxy at z= 3.15 for which Lyman-continuum (LyC) radiation is significantly detected in deep Keck/LRIS spectroscopy. We find no evidence of contamination from a lower-redshift interloper close to the line of sight in the high signal-to-noise spectrum of Q1549-C25. Furthermore, the morphology of Q1549-C25 in V sub(606), J sub(125), and H sub(160)Hubble Space Telescope(HST) imaging reveals that the object consists of a single, isolated component within 1''. In combination, these data indicate Q1549-C25 as a clean spectroscopic detection of LyC radiation, only the second such object discovered to date at z~ 3. We model the spectral energy distribution of Q1549-C25, finding evidence of negligible dust extinction, an age (assuming continuous star formation) of ~1 Gyr, and a stellar mass of Mlow * = 7.9 x 10 super(9)Mmiddot in circle. Although it is not possible to derive strong constraints on the absolute escape fraction of LyC emission, f sub(esc)(LyC), from a single object, we use simulations of intergalactic and circumgalactic absorption to infer f sub(esc)(LyC) > or =, slanted 0.51 at 95% confidence. The combination of deep Keck/LRIS spectroscopy and Hubble Space Telescope imaging is required to assemble a larger sample of objects like Q1549-C25, and obtain robust constraints on the average f sub(esc)(LyC) at z~ 3 and beyond.