Plant-insect interactions are ubiquitous, and have been studied intensely because of their relevance to damage and pollination in agricultural plants, and to the ecology and evolution of biodiversity. Variation within species can affect the outcome of these interactions. Specific genes and chemicals that mediate these interactions have been identified, but studies of genome- or metabolome-wide intraspecific variation might be necessary to better explain patterns of host-plant use and adaptation in the wild. Here, we present such a study. We assess the consequences of genome-wide genetic variation in the model plant Medicago truncatula for Lycaeides melissa caterpillar growth and survival (larval performance). Using a rearing experiment and a whole-genome SNP data set (>5 million SNPs), we find that polygenic variation in M. truncatula explains 9-41% of the observed variation in caterpillar growth and survival. Genetic correlations among caterpillar performance and other plant traits, including structural defenses and some anonymous chemical features, suggest that multiple M. truncatula alleles have pleiotropic effects on plant traits and caterpillar performance (or that substantial linkage disequilibrium exists among distinct loci affecting subsets of these traits). A moderate proportion of the genetic effect of M. truncatula alleles on L. melissa performance can be explained by the effect of these alleles on the plant traits we measured, especially leaf toughness. Taken together, our results show that intraspecific genetic variation in M. truncatula has a substantial effect on the successful development of L. melissa caterpillars (i.e., on a plant-insect interaction), and further point toward traits mediating this genetic effect.