  The bright soft X-ray transient Nova Muscae 1991 was intensively observed
during its entire 8-month outburst using the Large Area Counter (LAC) onboard
the Ginga satellite. Recently, we obtained accurate estimates of the mass of
the black hole primary, the orbital inclination angle of the system, and the
distance. Using these crucial input data and Ginga X-ray spectra, we have
measured the spin of the black hole using the continuum-fitting method. For
four X-ray spectra of extraordinary quality we have determined the
dimensionless spin parameter of the black hole to be a/M = 0.63 (-0.19, +0.16)
(1 sigma confidence level), a result that we confirm using eleven additional
spectra of lower quality. Our spin estimate challenges two published results:
It is somewhat higher than the value predicted by a proposed relationship
between jet power and spin; and we find that the spin of the black hole is
decidedly prograde, not retrograde as has been claimed.
