Pluto and its satellite, Charon (discovered in 1978; ref. 1), appear to form a double planet, rather than a hierarchical planet/satellite couple. Charon is about half Pluto's size and about one-eighth its mass. The precise radii of Pluto and Charon have remained uncertain, leading to large uncertainties on their densities. Although stellar occultations by Charon are in principle a powerful way of measuring its size, they are rare, as the satellite subtends less than 0.3 microradians (0.06 arcsec) on the sky. One occultation (in 1980) yielded a lower limit of 600 km for the satellite's radius, which was later refined to 601.5 km (ref. 4). Here we report observations from a multi-station stellar occultation by Charon, which we use to derive a radius, RC = 603.6 ± 1.4 km (1σ), and a density of ρ = 1.71 ± 0.08 g cm-3. This occultation also provides upper limits of 110 and 15 (3σ) nanobar for an atmosphere around Charon, assuming respectively a pure nitrogen or pure methane atmosphere.