Why does the Y chromosome harbor so few functional loci? Evolutionary theory predicts that Y chromosomes degenerate because they lack genetic recombination. Both positive and negative selection models have been invoked to explain this degeneration, as both can result in the recurrent fixation of linked deleterious mutations on a nonrecombining Y chromosome. To distinguish between these models, I investigated patterns of nucleotide variability along 37 kb of the recently formed neo-Y chromosome in Drosophila miranda. Levels of nucleotide variability on this chromosome are 30 times lower than in highly recombining portions of the genome. Both positive and negative selection models can result in reduced variability levels, but their effects on the frequency spectrum of mutations differ. Using coalescent simulations, I show that the patterns of nucleotide variability on the neo-Y chromosome are unlikely under deleterious mutation models (including background selection and Muller's ratchet) but are expected under recent positive selection. These results implicate positive selection as an important force driving the degeneration of Y chromosomes; adaptation at a few loci, possibly increasing male fitness, occurs at the cost of most other genes on this chromosome.