M82 X-1, the brightest X-ray source in the galaxy M82, has been thought to be an intermediate-mass black hole (100 to 10,000 solar masses) because of its extremely high luminosity and variability characteristics(1-6), although some models suggest that its mass may be only about 20 solar masses(3,7). The previous mass estimates were based on scaling relations that use low-frequency characteristic time-scales which have large intrinsic uncertainties(8,9). For stellar-mass black holes, we know that the high-frequency quasi-periodic oscillations (100-450 hertz) in the X-ray emission that occur in a 3: 2 frequency ratio are stable and scale in frequency inversely with black hole mass with a reasonably small dispersion(10-15). The discovery of such stable oscillations thus potentially offers an alternative and less ambiguous means of mass determination for intermediate-mass black holes, but has hitherto not been realized. Here we report stable, twin-peak (3: 2 frequency ratio) X-ray quasi-periodic oscillations from M82 X-1 at frequencies of 3.32+/-0.06 hertz and 5.07+/-0.06 hertz. Assuming that we can extrapolate the inverse-mass scaling that holds for stellar-mass black holes, we estimate the black hole mass of M82 X-1 to be 428+/-105 solar masses. In addition, we can estimate the mass using the relativistic precession model, from which we get a value of 415+/-63 solar masses.