The detection of footprints of natural selection in genetic polymorphism data is fundamental to understanding the genetic basis of adaptation, and has important implications for human health. The standard approach has been to reject neutrality in favor of selection if the pattern of variation at a candidate locus was significantly different from the predictions of the standard neutral model. The problem is that the standard neutral model assumes more than just neutrality, and it is almost always possible to explain the data using an alternative neutral model with more complex demography. Today's wealth of genomic polymorphism data, however, makes it possible to dispense with models altogether by simply comparing the pattern observed at a candidate locus to the genomic pattern, and rejecting neutrality if the pattern is extreme. Here, we utilize this approach on a truly genomic scale, comparing a candidate locus to thousands of alleles throughout the Arabidopsis thaliana genome. We demonstrate that selection has acted to increase the frequency of early-flowering alleles at the vernalization requirement locus FRIGIDA. Selection seems to have occurred during the last several thousand years, possibly in response to the spread of agriculture. We introduce a novel test statistic based on haplotype sharing that embraces the problem of population structure, and so should be widely applicable.