The human Y chromosome, transmitted clonally through males, contains far fewer genes than the sexually recombining autosome from which it evolved. The enormity of this evolutionary decline has led to predictions that the Y chromosome will be completely bereft of functional genes within ten million years. Although recent evidence of gene conversion within massive Y-linked palindromes runs counter to this hypothesis, most unique Y-linked genes are not situated in palindromes and have no gene conversion partners. The "impending demise" hypothesis thus rests on understanding the degree of conservation of these genes. Here we find, by systematically comparing the DNA sequences of unique, Y-linked genes in chimpanzee and human, which diverged about six million years ago, evidence that in the human lineage, all such genes were conserved through purifying selection. In the chimpanzee lineage, by contrast, several genes have sustained inactivating mutations. Gene decay in the chimpanzee lineage might be a consequence of positive selection focused elsewhere on the Y chromosome and driven by sperm competition.