We present the first luminous, spatially resolved binary quasar that clearly inhabits an ongoing galaxy merger. SDSS J125455.09+084653.9 and SDSS J125454.87+084652.1 (SDSS J1254+0846 hereafter) are two luminous z = 0.44 radio-quiet quasars, with a radial velocity difference of just 215 km s^–1, separated on the sky by 21 kpc in a disturbed host galaxy merger showing obvious tidal tails. The pair was targeted as part of a complete sample of binary quasar candidates with small transverse separations drawn from SDSS DR6 photometry. We present follow-up optical imaging which shows broad, symmetrical tidal arm features spanning some 75 kpc at the quasars' redshift. Previously, the triggering of two quasars during a merger had only been hypothesized but our observations provide strong evidence of such an event. SDSS J1254+0846, as a face-on, pre-coalescence merger hosting two luminous quasars separated by a few dozen kpc, provides a unique opportunity to probe quasar activity in an ongoing gas-rich merger. Numerical modeling suggests that the system consists of two massive disk galaxies prograde to their mutual orbit, caught during the first passage of an active merger. This demonstrates rapid black hole growth during the early stages of a merger between galaxies with pre-existing bulges. Neither of the two luminous nuclei show significant intrinsic absorption by gas or dust in our optical or X-ray observations, illustrating that not all merging quasars will be in an obscured, ultraluminous phase. We find that the Eddington ratio for the fainter component B is rather normal, while for the A component L/L _Edd is quite (>3σ) high compared to quasars of similar luminosity and redshift, possibly evidence for strong merger-triggered accretion. More such mergers should be identifiable at higher redshifts using binary quasars as tracers.