The development of a quantitative understanding of viral evolution and the fitness landscape in HIV-1 drug resistance is a formidable challenge given the large number of available drugs and drug resistance mutations. We analyzed a dataset measuring the in vitro fitness of 70,081 virus samples isolated from HIV-1 subtype B infected individuals undergoing routine drug resistance testing. We assayed virus samples for in vitro replicative capacity in the absence of drugs as well as in the presence of 15 individual drugs. We employed a generalized kernel ridge regression to estimate main fitness effects and epistatic interactions of 1,859 single amino acid variants found within the HIV-1 protease and reverse transcriptase sequences. Models including epistatic interactions predict an average of 54.8% of the variance in replicative capacity across the 16 different environments and substantially outperform models based on main fitness effects only. We find that the fitness landscape of HIV-1 protease and reverse transcriptase is characterized by strong epistasis.