Results from the first study of isolated-photon + jet correlations in relativistic heavy ion collisions are reported. The analysis uses data from PbPb collisions at a centre-of-mass energy of 2.76 TeV per nucleon pair corresponding to an integrated luminosity of 150 mu b - 1 recorded by the CMS experiment at the LHC. For events containing an isolated photon with transverse momentum p T gamma > 60 GeV / c and an associated jet with p T Jet > 30 GeV / c , the photon + jet p T imbalance is studied as a function of collision centrality and compared to pp data and pythia calculations at the same collision energy. Using the p T gamma of the isolated photon as an estimate of the momentum of the associated parton at production, this measurement allows an unbiased characterisation of the in-medium parton energy loss. For more central PbPb collisions, a significant decrease in the ratio p T Jet / p T gamma relative to that in the pythia reference is observed. Furthermore, significantly more p T gamma > 60 GeV / c photons in PbPb are observed not to have an associated p T Jet > 30 GeV / c jet, compared to the reference. However, no significant broadening of the photon + jet azimuthal correlation is observed.