  Building upon a new dynamical model for the X-ray binary LMC X-3, we measure
the spin of its black hole primary via the continuum-fitting method. We
consider over one thousand thermal-state RXTE X-ray spectra of LMC X-3. Using a
large subset of these spectra, we constrain the spin parameter of the black
hole to be spin = 0.21(+0.18,-0.22), 90% confidence. Our estimate of the
uncertainty in spin takes into account a wide range of systematic errors. We
discuss evidence for a correlation between a black hole's spin and the
complexity of its X-ray spectrum.
