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 quantify Darwinian fitness under a high-temperature challenge for over 65,000 yeast strains each carrying a unique variant of the single-copy tRNA gene at its native genomic location. Approximately 1% of single point mutations in the gene are beneficial, while 42% are deleterious. Almost half of all mutation pairs exhibit significant epistasis, which has a strong negative bias except when the mutations occur at Watson-Crick paired sites. Fitness is correlated with the predicted fraction of correctly folded tRNA molecules, revealing a biophysical basis of the fitness landscape.