The process pˉp -> photon + jet + X as studied by the D0 detector at the Fermilab Tevatron collider at center-of-mass energy √s=1.96TeV. Photons are reconstructed in the central rapidity region |yγ|<1.0 with transverse momenta in the range 30--400 GeV, while jets are reconstructed in either the central |yjet|<0.8 or forward 1.5<|yjet|<2.5 rapidity intervals with pjet⊥>15GeV. The differential cross section d3σ/dpγ⊥dyγdyjet is measured as a function of pγ⊥ in four regions, differing by the relative orientations of the photon and the jet. MC predictions have trouble with simultaneously describing the measured normalization and pγ⊥ dependence of the cross section in any of the four measured regions.