Fitness landscapes describe the genotype-fitness relationship and represent major determinants of evolutionary trajectories. However, the vast genotype space, coupled with the difficulty of measuring fitness, has hindered the empirical determination of fitness landscapes. Combining precise gene replacement and next-generation sequencing, we quantified Darwinian fitness under a high-temperature challenge for more than 65,000 yeast strains, each carrying a unique variant of the single-copy tRNA(CCU)(Arg) gene at its native genomic location. Approximately 1% of single point mutations in the gene were beneficial and 42% were deleterious. Almost half of all mutation pairs exhibited statistically significant epistasis, which had a strong negative bias, except when the mutations occurred at Watson-Crick paired sites. Fitness was broadly correlated with the predicted fraction of correctly folded transfer RNA (tRNA) molecules, thereby revealing a biophysical basis of the fitness landscape.