Stony corals, which form the framework for modern reefs, are classified as Scleractinia (Cnidaria, Anthozoa, and Hexacorallia) in reference to their external aragonitic skeletons. However, persistent notions, collectively known as the “naked coral” hypothesis, hold that the scleractinian skeleton does not define a natural group. Three main lines of evidence have suggested that some stony corals are more closely related to one or more of the soft-bodied hexacorallian groups than they are to other scleractinians: (i) morphological similarities; (ii) lack of phylogenetic resolution in molecular analyses of scleractinians; and (iii) discrepancy between the commencement of a diverse scleractinian fossil record at 240 million years ago (Ma) and a molecule-based origination of at least 300 Ma. No molecular evidence has been able to clearly reveal relationships at the base of a well supported clade composed of scleractinian lineages and the nonskeletonized Corallimorpharia. We present complete mitochondrial genome data that provide strong evidence that one clade of scleractinians is more closely related to Corallimorpharia than it is to a another clade of scleractinians. Thus, the scleractinian skeleton, which we estimate to have originated between 240 and 288 Ma, was likely lost in the ancestry of Corallimorpharia. We estimate that Corallimorpharia originated between 110 and 132 Ma during the late- to mid-Cretaceous, coinciding with high levels of oceanic CO(2), which would have impacted aragonite solubility. Corallimorpharians escaped extinction from aragonite skeletal dissolution, but some modern stony corals may not have such fortunate fates under the pressure of increased anthropogenic CO(2) in the ocean.