First measurements of the differential cross sections for the inclusive production of a photon in association with a heavy quark (c, b) jet are presented, covering photon transverse momenta 30-150 GeV, photon rapidities | y_gamma| < 1.0, jet rapidities |y_jet| < 0.8, and jet transverse momenta pT_jet > 15 GeV. The results are based on an integrated luminosity of 1 fb^-1 in ppbar collisions at sqrt(s)=1.96 TeV recorded with the D0 detector at the Fermilab Tevatron Collider. The results are compared with next-to-leading order perturbative QCD predictions.