Oat (Avena sativa L.) has a high concentration of oils, comprised primarily of healthful unsaturated oleic and linoleic fatty acids. To accelerate oat plant breeding efforts, we sought to identify loci associated with variation in fatty acid composition, defined as the types and quantities of fatty acids. We genotyped a panel of 500 oat cultivars with genotyping-by-sequencing and measured the concentrations of ten fatty acids in these oat cultivars grown in two environments. Measurements of individual fatty acids were highly correlated across samples, consistent with fatty acids participating in shared biosynthetic pathways. We leveraged these phenotypic correlations in two multivariate genome-wide association study (GWAS) approaches. In the first analysis, we fitted a multivariate linear mixed model for all ten fatty acids simultaneously while accounting for population structure and relatedness among cultivars. In the second, we performed a univariate association test for each principal component (PC) derived from a singular value decomposition of the phenotypic data matrix. To aid interpretation of results from the multivariate analyses, we also conducted univariate association tests for each trait. The multivariate mixed model approach yielded 148 genome-wide significant single-nucleotide polymorphisms (SNPs) at a 10% false-discovery rate, compared to 129 and 73 significant SNPs in the PC and univariate analyses, respectively. Thus, explicit modeling of the correlation structure between fatty acids in a multivariate framework enabled identification of loci associated with variation in seed fatty acid concentration that were not detected in the univariate analyses. Ultimately, a detailed characterization of the loci underlying fatty acid variation can be used to enhance the nutritional profile of oats through breeding.