  We report the observation at the Relativistic Heavy Ion Collider (RHIC) of
suppression of back-to-back correlations in the direct photon+jet channel in
Au+Au relative to p+p collisions. Two-particle correlations of direct photon
triggers with associated hadrons are obtained by statistical subtraction of the
decay photon-hadron background. The initial momentum of the away-side parton is
tightly constrained, because the parton-photon pair exactly balance in momentum
at leading order in perturbative quantum chromodynamics (pQCD), making such
correlations a powerful probe of the in-medium parton energy loss. The
away-side nuclear suppression factor, I_AA, in central Au+Au collisions, is
0.32 +/- 0.12(stat) +/- 0.09(syst) for hadrons of 3 < p_T < 5 in coincidence
with photons of 5 < p_T < 15 GeV/c. The suppression is comparable to that
observed for high-p_T single hadrons and dihadrons. The direct photon
associated yields in p+p collisions scale approximately with the momentum
balance, z_T = p_T^hadron/p_T^photon, as expected for a measure of the
away-side parton fragmentation function. We compare to Au+Au collisions for
which the momentum balance dependence of the nuclear modification should be
sensitive to the path-length dependence of parton energy loss.
