A well-known mechanism through which new protein-coding genes originate is by modification of pre-existing genes, e.g. by duplication or horizontal transfer. In contrast, many viruses generate protein-coding genes de novo, via the overprinting of a new reading frame onto an existing ("ancestral") frame. This mechanism is thought to play an important role in viral pathogenicity, but has been poorly explored, perhaps because identifying the de novo frames is very challenging. Therefore, a new approach to detect them was needed. We assembled a reference set of overlapping genes for which we could reliably determine the ancestral frames, and found that their codon usage was significantly closer to that of the rest of the viral genome than the codon usage of de novo frames. Based on this observation, we designed a method that allowed the identification of de novo frames based on their codon usage with a very good specificity, but intermediate sensitivity. Using our method, we predicted that the Rex gene of deltaretroviruses has originated de novo by overprinting the Tax gene. Intriguingly, several genes in the same genomic region have also originated de novo and encode proteins that regulate the functions of Tax. Such "gene nurseries" may be common in viral genomes. Finally, our results confirm that the genomic GC content is not the only determinant of codon usage in viruses and suggest that a constraint linked to translation must influence codon usage.