Prompt photon production in root S-NN = 2.76-TeV Pb + Pb collisions has been measured by the ATLAS experiment at the Large Hadron Collider using data collected in 2011 with an integrated luminosity of 0.14 nb(-1). Inclusive photon yields, scaled by the mean nuclear thickness function, are presented as a function of collision centrality and transverse momentum in two pseudorapidity intervals, vertical bar eta vertical bar < 1.37 and 1.52 <= vertical bar eta vertical bar < 2.37. The scaled yields in the two pseudorapidity intervals, as well as the ratios of the forward yields to those at midrapidity, are compared to the expectations from next-to-leading-order perturbative QCD (pQCD) calculations. The measured cross sections agree well with the predictions for proton-proton collisions within statistical and systematic uncertainties. Both the yields and the ratios are also compared to two other pQCD calculations, one which uses the isospin content appropriate to colliding lead nuclei and another which includes nuclear modifications to the nucleon parton distribution functions.