  We report on a deep Suzaku observation of the stellar-mass black hole GX
339-4 in outburst. A clear, strong, relativistically-shaped iron emission line
from the inner accretion disk is observed. The broad-band disk reflection
spectrum revealed is one of the most sensitive yet obtained from an accreting
black hole. We fit the Suzaku spectra with a physically-motivated disk
reflection model, blurred by a new relativistic line function in which the
black hole spin parameter is a variable. This procedure yielded a black hole
spin parameter of a = 0.89 +/- 0.04. Joint modeling of these Suzaku spectra and
prior XMM-Newton spectra obtained in two different outburst phases yields a
spin parameter of a = 0.93 +/- 0.01. The degree of consistency between these
results suggests that disk reflection models allow for spin measurements that
are not strongly biased by scattering effects. We suggest that the best value
of the black hole spin parameter is a = 0.93 +/- 0.01 (statistical) +/- 0.04
(systematic). Although preliminary, these results represent the first direct
measurement of non-zero spin in a stellar-mass black hole using relativistic
line modeling.
