We report the discovery of a 61-Jupiter-mass brown dwarf, which transits its F8V host star, WASP-30, every 4.16 days. From a range of age indicators we estimate the system age to be 1-2 Gyr. We derive a radius (0.89 +/- 0.02 RJup) for the companion that is consistent with that predicted (0.914 RJup) by a model of a 1-Gyr-old, non-irradiated brown dwarf with a dusty atmosphere. The location of WASP-30b in the minimum of the mass-radius relation is consistent with the quantitative prediction of Chabrier & Baraffe (2000), thus confirming the theory.