Prompt photons are a powerful tool to study heavy ion collisions. Their production rates provide access to the initial state parton distribution functions and also provide a means to calibrate the expected energy of jets that are produced in the medium. The ATLAS detector measures photons with its hermetic, longitudinally segmented calorimeter, which gives excellent spatial and energy resolutions, and detailed information about the shower shape of each measured photon. This provides significant rejection against the expected background from the decays of neutral pions in jets. Rejection against jet fragmentation products is further enhanced by requiring candidate photons to be isolated. First results on the spectra of isolated prompt photons from a dataset with an integrated luminosity of approximately 0.13 nb^-1 of lead-lead collisions at sqrt(s_NN)=2.76 TeV are shown as a function of transverse momentum and centrality. The measured spectra are compared to expectations from perturbative QCD calculations.