  Most ultraluminous X-ray sources (ULXs) display a typical set of properties
not seen in Galactic stellar-mass black holes (BHs): higher luminosity Lx > 3
10^39 erg/s, unusually soft X-ray components (kT < 0.3 keV) and a
characteristic downturn in their spectra above ~ 5 keV. Such puzzling
properties have been interpreted either as evidence of intermediate-mass BHs,
or as emission from stellar-mass BHs accreting above their Eddington limit,
analogous to some Galactic BHs at peak luminosity. Recently, a very soft X-ray
spectrum has been observed in a rare and transient stellar-mass BH. Here we
show that the X-ray source P13 in the galaxy NGC\,7793 is in a ~ 64 day period
binary and exhibits all three canonical properties of ULXs. By modelling the
strong optical and UV modulations due to X-ray heating of the B9Ia donor star,
we constrain the BH mass to less than 15 solar masses. Our results demonstrate
that in P13, soft thermal emission and spectral curvature are indeed signatures
of supercritical accretion. By analogy, ULXs with similar X-ray spectra and
luminosities of up to a few 10^40 erg/s can be explained by supercritical
accretion onto massive stellar BHs.
