For the first time, a full one-loop calculation of the process chi chi --> 2 gamma is performed, where chi is the lightest neutralino in the minimal supersymmetric extension of the Standard Model. This process is of interest for dark matter detection, since it would give a sharp gamma ray line with E-gamma = m(chi). We improve upon and correct published formulas, and give cross sections for supersymmetric models with chi masses between 30 GeV and several TeV. We find a new contribution, previously neglected, which enhances the 2 gamma rate for TeV higgsinos by up to an order of magnitude. As a byproduct, we obtain a new expression for the related process chi chi --> 2 gluons, which on the other hand can be smaller than previously calculated. There has been a recent claim that evidence for a 3.5 TeV higgsino annihilating into a gamma line may already exist from balloon emulsion and Air Cherenkov Telescope data. We comment on attractive features and problems with this interpretation. (C) 1997 Published by Elsevier Science B.V. PACS: 95.35.+d; 14.80.Ly.