Overlapping genes in viruses maximize the coding capacity of their genomes and allow the generation of new genes without major increases in genome size. Despite their importance, the evolution and function of overlapping genes are often not well understood, in part due to difficulties in their detection. In addition, most bioinformatic approaches for the detection of overlapping genes require the comparison of multiple genome sequences that may not be available in metagenomic surveys of virus biodiversity. We introduce a simple new method for identifying candidate functional overlapping genes using single virus genome sequences. Our method uses randomization tests to estimate the expected length of open reading frames and then identifies overlapping open reading frames that significantly exceed this length and are thus predicted to be functional. We applied this method to 2548 reference RNA virus genomes and find that it has both high sensitivity and low false discovery for genes that overlap by at least 50 nucleotides. Notably, this analysis provided evidence for 29 previously undiscovered functional overlapping genes, some of which are coded in the antisense direction suggesting there are limitations in our current understanding of RNA virus replication.