The modulation of fitness by single mutational substitutions during environmental change is the most fundamental consequence of natural selection. The antagonistic tradeoffs of pleiotropic mutations that can be selected under changing environments therefore lie at the foundation of evolutionary biology. However, the molecular basis of fitness tradeoffs is rarely determined in terms of how these pleiotropic mutations affect protein structure. Here we use an interdisciplinary approach to study how antagonistic pleiotropy and protein function dictate a fitness tradeoff. We challenged populations of an RNA virus, bacteriophage Φ6, to evolve in a novel temperature environment where heat shock imposed extreme virus mortality. A single amino acid substitution in the viral lysin protein P5 (V207F) favored improved stability, and hence survival of challenged viruses, despite a concomitant tradeoff that decreased viral reproduction. This mutation increased the thermostability of P5. Crystal structures of wild-type, mutant, and ligand-bound P5 reveal the molecular basis of this thermostabilization--the Phe207 side chain fills a hydrophobic cavity that is unoccupied in the wild-type--and identify P5 as a lytic transglycosylase. The mutation did not reduce the enzymatic activity of P5, suggesting that the reproduction tradeoff stems from other factors such as inefficient capsid assembly or disassembly. Our study demonstrates how combining experimental evolution, biochemistry, and structural biology can identify the mechanisms that drive the antagonistic pleiotropic phenotypes of an individual point mutation in the classic evolutionary tug-of-war between survival and reproduction.