Although many animals communicate vocally, no extant creature rivals modern humans in language ability. Therefore, knowing when and under what evolutionary pressures our capacity for language evolved is of great interest. Here, we find that our closest extinct relatives, the Neandertals, share with modern humans two evolutionary changes in FOXP2, a gene that has been implicated in the development of speech and language. We furthermore find that in Neandertals, these changes lie on the common modern human haplotype, which previously was shown to have been subject to a selective sweep. These results suggest that these genetic changes and the selective sweep predate the common ancestor (which existed about 300,000-400,000 years ago) of modern human and Neandertal populations. This is in contrast to more recent age estimates of the selective sweep based on extant human diversity data. Thus, these results illustrate the usefulness of retrieving direct genetic information from ancient remains for understanding recent human evolution.