Complete mitochondrial genomic sequences are reported from 12 members in the four families of the reptile group Amphisbaenia. Analysis of 11,946 aligned nucleotide positions (5797 informative) produces a robust phylogenetic hypothesis. The family Rhineuridae is basal and Bipedidae is the sister taxon to the Amphisbaenidae plus Trogonophidae. Amphisbaenian reptiles are surprisingly old, predating the breakup of Pangaea 200 million years before present, because successive basal taxa (Rhineuridae and Bipedidae) are situated in tectonic regions of Laurasia and nested taxa (Amphisbaenidae and Trogonophidae) are found in Gondwanan regions. Thorough sampling within the Bipedidae shows that it is not tectonic movement of Baja California away from the Mexican mainland that is primary in isolating Bipes species, but rather that primary vicariance occurred between northern and southern groups. Amphisbaenian families show parallel reduction in number of limbs and Bipes species exhibit parallel reduction in number of digits. A measure is developed for comparing the phylogenetic information content of various genes. A synapomorphic trait defining the Bipedidae is a shift from the typical vertebrate mitochondrial gene arrangement to the derived state of trnE and nad6. In addition, a tandem duplication of trnT and trnP is observed in Bipes biporus with a pattern of pseudogene formation that varies among populations. The first case of convergent rearrangement of the mitochondrial genome among animals demonstrated by complete genomic sequences is reported. Relative to most vertebrates, the Rhineuridae has the block nad6, trnE switched in order with the block cob, trnT, trnP, as they are in birds.