The genomes of many RNA viruses contain abundant secondary structures that have been shown to be important for understanding the evolution of noncoding regions and synonymous sites. However, the consequences for protein evolution are less well understood. Recently, the secondary structure of the HIV-1 RNA genome has been experimentally determined. Using this information, here we show that RNA structure and proteins do not evolve independently. A negative correlation exists between the extent of base pairing in the genomic RNA and amino acid variability. Relaxed RNA structures may favor the accumulation of genetic variation in proteins and, conversely, sequence changes driven by positive selection at the protein level may disrupt existing RNA structures. We also find that breakage of RNA base pairs might impose a fitness cost to drug resistance mutations in the protease and reverse transcriptase genes, thereby limiting their spread among untreated patients. Characterizing the evolutionary trade-offs between the selective pressures acting at the RNA and protein levels will help us to better understand the variability and evolution of HIV-1.