One of the most powerful and commonly used approaches for detecting local adaptation in the genome is the identification of extreme allele frequency differences between populations. In this article, we present a new maximum likelihood method for finding regions under positive selection. It is based on a Gaussian approximation to allele frequency changes and it incorporates admixture between populations. The method can analyze multiple populations simultaneously and retains power to detect selection signatures specific to ancestry components that are not representative of any extant populations. Using simulated data, we compare our method to related approaches, and show that it is orders of magnitude faster than the state-of-the-art, while retaining similar or higher power for most simulation scenarios. We also apply it to human genomic data and identify loci with extreme genetic differentiation between major geographic groups. Many of the genes identified are previously known selected loci relating to hair pigmentation and morphology, skin, and eye pigmentation. We also identify new candidate regions, including various selected loci in the Native American component of admixed Mexican-Americans. These involve diverse biological functions, such as immunity, fat distribution, food intake, vision, and hair development.