Searching for genetic variants with unusual differentiation between subpopulations is an established approach for identifying signals of natural selection. However, existing methods generally require discrete subpopulations. We introduce a method that infers selection using principal components (PCs) by identifying variants whose differentiation along top PCs is significantly greater than the null distribution of genetic drift. To enable the application of this method to large data sets, we developed the FastPCA software, which employs recent advances in random matrix theory to accurately approximate top PCs while reducing time and memory cost from quadratic to linear in the number of individuals, a computational improvement of many orders of magnitude. We apply FastPCA to a cohort of 54,734 European Americans, identifying 5 distinct subpopulations spanning the top 4 PCs. Using the PC-based test for natural selection, we replicate previously known selected loci and identify three new genome-wide significant signals of selection, including selection in Europeans at the ADH1B gene. The derived allele of the coding variant rs1229984 has previously been associated to a decreased risk of alcoholism and shown to be under selection in East Asians; we show that it is a rare example of independent evolution on two continents. We also detect new selection signals at IGFBP3 and IGH, which have also previously been associated to human disease.