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 inverse microbarns recorded by the CMS experiment at the LHC. For events containing an isolated photon with transverse momentum pt(gamma) > 60 GeV and an associated jet with pt(Jet) > 30 GeV, the photon + jet pt imbalance is studied as a function of collision centrality and compared to pp data and PYTHIA calculations at the same collision energy. Using the pt(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 pt(Jet)/pt(gamma) relative to that in the PYTHIA reference is observed. Furthermore, significantly more pt(gamma) > 60 GeV photons in PbPb are observed not to have an associated pt(Jet) > 30 GeV jet, compared to the reference. However, no significant broadening of the photon + jet azimuthal correlation is observed.