Documented cases of convergent molecular evolution due to selection are fairly unusual, and examples to date have involved only a few amino acid positions. However, because convergence mimics shared ancestry and is not accommodated by current phylogenetic methods, it can strongly mislead phylogenetic inference when it does occur. Here, we present a case of extensive convergent molecular evolution between snake and agamid lizard mitochondrial genomes that overcomes an otherwise strong phylogenetic signal. Evidence from morphology, nuclear genes, and most sites in the mitochondrial genome support one phylogenetic tree, but a subset of mostly amino acid-altering substitutions (primarily at the first and second codon positions) across multiple mitochondrial genes strongly supports a radically different phylogeny. The relevant sites generally evolved slowly but converged between ancient lineages of snakes and agamids. We estimate that approximately 44 of 113 predicted convergent changes distributed across all 13 mitochondrial protein-coding genes are expected to have arisen from nonneutral causes-a remarkably large number. Combined with strong previous evidence for adaptive evolution in snake mitochondrial proteins, it is likely that much of this convergent evolution was driven by adaptation. These results indicate that nonneutral convergent molecular evolution in mitochondria can occur at a scale and intensity far beyond what has been documented previously, and they highlight the vulnerability of standard phylogenetic methods to the presence of nonneutral convergent sequence evolution.