Vertebrates possess diverse sex-determining systems, which differ in evolutionary stability among particular groups. It has been suggested that poikilotherms possess more frequent turnovers of sex chromosomes than homoiotherms, whose effective thermoregulation can prevent the emergence of the sex reversals induced by environmental temperature. Squamate reptiles used to be regarded as a group with an extensive variability in sex determination; however, we document how the rather old radiation of lizards from the genus Anolis, known for exceptional ecomorphological variability, was connected with stability in sex chromosomes. We found that 18 tested species, representing most of the phylogenetic diversity of the genus, share the gene content of their X chromosomes. Furthermore, we discovered homologous sex chromosomes in species of two genera (Sceloporus and Petrosaurus) from the family Phrynosomatidae, serving here as an outgroup to Anolis. We can conclude that the origin of sex chromosomes within iguanas largely predates the Anolis radiation and that the sex chromosomes of iguanas remained conserved for a significant part of their evolutionary history. Next to therian mammals and birds, Anolis lizards therefore represent another adaptively radiated amniote clade with conserved sex chromosomes. We argue that the evolutionary stability of sex-determining systems may reflect an advanced stage of differentiation of sex chromosomes rather than thermoregulation strategy.