Precisely defining how viral mutations affect HIV's sensitivity to antibodies is vital to the development and evaluation of vaccines and antibody immunotherapeutics. But despite great effort, a full map of escape mutants has not yet been delineated for even a single anti-HIV antibody. Here we describe a massively parallel experimental approach to quantify how all single amino-acid mutations to Envelope (Env) affect HIV's sensitivity to a neutralizing antibody. We applied this approach to PGT151 and identified novel sites of escape in addition to those previously defined by structural and functional studies, such as glycans at sites 611 and 637, residue 647, and sites in the fusion peptide. Evaluating the effect of each amino acid at each site lends insight into the biochemical basis of escape throughout the epitope. Thus, comprehensive mapping of HIV antibody escape gives a quantitative, mutation-level view of the ways that Env can evade neutralization.