The bright soft X-ray transient Nova Muscae 1991 was intensively observed during its entire eight-month outburst using the Large Area Counter on board 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}* ={0.63}-0.19+0.16 (1s confidence level), a result that we confirm using 11 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.
