There are two proposed explanations for ultraluminous X-ray sources (ULXs) with luminosities in excess of 10(39) erg s(-1). They could be intermediate-mass black holes (more than 100-1,000 solar masses, M sun symbol) radiating at sub-maximal (sub-Eddington) rates, as in Galactic black-hole X-ray binaries but with larger, cooler accretion disks. Alternatively, they could be stellar-mass black holes radiating at Eddington or super-Eddington rates. On its discovery, M 101 ULX-1 had a luminosity of 3 × 10(39) erg s(-1) and a supersoft thermal disk spectrum with an exceptionally low temperature--uncomplicated by photons energized by a corona of hot electrons--more consistent with the expected appearance of an accreting intermediate-mass black hole. Here we report optical spectroscopic monitoring of M 101 ULX-1. We confirm the previous suggestion that the system contains a Wolf-Rayet star, and reveal that the orbital period is 8.2 days. The black hole has a minimum mass of 5 M sun symbol, and more probably a mass of 20 M sun symbol-30 M sun symbol, but we argue that it is very unlikely to be an intermediate-mass black hole. Therefore, its exceptionally soft spectra at high Eddington ratios violate the expectations for accretion onto stellar-mass black holes. Accretion must occur from captured stellar wind, which has hitherto been thought to be so inefficient that it could not power an ultraluminous source.