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The process pp → γ + jet + X is studied using 1.0 fb−1 of data collected by the D0 detector at the Fermilab Tevatron pp collider at a center-of-mass energy √s = 1.96 TeV. Photons are reconstructed in the central rapidity region |yγ | < 1.0 with transverse momenta in the range 30 < pγT < 400 GeV while jets are reconstructed in either the central |yjet| < 0.8 or forward 1.5 < |yjet| < 2.5 rapidity intervals with pjetT > 15 GeV. The differential cross section d3σ/dpγT dyγ dyjet is measured as a function of pγT in four regions, differing by the relative orientations of the photon and the jet in rapidity. Ratios between the differential cross sections in each region are also presented. Next-to-leading order QCD predictions using different parameterizations of parton distribution functions and theoretical scale choices are compared to the data. The predictions do not simultaneously describe the measured normalization and pγT dependence of the cross section in the four measured regions.