The evolutionary origin of “orphan” genes, genes that lack sequence similarity to any known gene, remains a mystery. One suggestion has been that most orphan genes evolve rapidly so that similarity to other genes cannot be traced after a certain evolutionary distance. This can be tested by examining the divergence rates of genes with different degrees of lineage specificity. Here the lineage specificity (LS) of a gene describes the phylogenetic distribution of that gene’s orthologues in related species. Highly lineage-specific genes will be distributed in fewer species in a phylogeny. In this study, we have used the complete genomes of seven ascomycotan fungi and two animals to define several levels of LS, such as Eukaryotes-core, Ascomycota-core, Euascomycetes-specific, Hemiascomycetes-specific, Aspergillus-specific, and Saccharomyces-specific. We compare the rates of gene evolution in groups of higher LS to those in groups with lower LS. Molecular evolutionary analyses indicate an increase in nonsynonymous nucleotide substitution rates in genes with higher LS. Several analyses suggest that LS is correlated with the evolutionary rate of the gene. This correlation is stronger than those of a number of other factors that have been proposed as predictors of a gene’s evolutionary rate, including the expression level of genes, gene essentiality or dispensability, and the number of protein-protein interactions. The accelerated evolutionary rates of genes with higher LS may reflect the influence of selection and adaptive divergence during the emergence of orphan genes. These analyses suggest that accelerated rates of gene evolution may be responsible for the emergence of apparently orphan genes.