The class of exotic Jupiter-mass planets that orbit very close to their parent stars were not explicitly expected before their discovery. The recently discovered transiting planet WASP-12b has a mass M = 1.4 +/- 0.1 Jupiter masses (M(J)), a mean orbital distance of only 3.1 stellar radii (meaning it is subject to intense tidal forces), and a period of 1.1 days. Its radius 1.79 +/- 0.09R(J) is unexpectedly large and its orbital eccentricity 0.049 +/- 0.015 is even more surprising because such close orbits are usually quickly circularized. Here we report an analysis of its properties, which reveals that the planet is losing mass to its host star at a rate of about 10(-7)M(J) per year. The planet's surface is distorted by the star's gravity and the light curve produced by its prolate shape will differ by about ten per cent from that of a spherical planet. We conclude that dissipation of the star's tidal perturbation in the planet's convective envelope provides the energy source for its large volume. We predict up to 10 mJy CO band-head (2.292 mum) emission from a tenuous disk around the host star, made up of tidally stripped planetary gas. It may also contain a detectable resonant super-Earth, as a hypothetical perturber that continually stirs up WASP-12b's eccentricity.