Brown dwarfs are considered to be `failed stars' in the sense that they are born with masses between the least massive stars (0.072 solar masses, Msolar) and the most massive planets (~0.013Msolar); they therefore serve as a critical link in our understanding of the formation of both stars and planets. Even the most fundamental physical properties of brown dwarfs remain, however, largely unconstrained by direct measurement. Here we report the discovery of a brown-dwarf eclipsing binary system, in the Orion Nebula star-forming region, from which we obtain direct measurements of mass and radius for these newly formed brown dwarfs. Our mass measurements establish both objects as brown dwarfs, with masses of 0.054 +/- 0.005Msolar and 0.034 +/- 0.003Msolar. At the same time, with radii relative to the Sun's of 0.669 +/- 0.034Rsolar and 0.511 +/- 0.026Rsolar, these brown dwarfs are more akin to low-mass stars in size. Such large radii are generally consistent with theoretical predictions for young brown dwarfs in the earliest stages of gravitational contraction. Surprisingly, however, we find that the less-massive brown dwarf is the hotter of the pair; this result is contrary to the predictions of all current theoretical models of coeval brown dwarfs.