This group is split into 2 families in PhyloCode. As promised, I will list them out here. In PhyloCode, "Chelidae" is the name of the "Cheloidea" Superfamily. The Superfamily then breaks off into Hesperochelida (the first 2 Subfamilies listed below) and Australochelida (the last 3 Subfamilies listed below). The PhyloCode designation makes a little sense once you see their distributions, but I'm still going to use Linnaean as the default. The turtles in Chelidae are split, 2 Subfamilies can be found in South America, and the other 3 can be found in Australia (thus, the PhyloCode designations). Also, if you were trying to look this stuff up on Wikipedia, it starts to get real outdated.
Chelidae breaks off into 5 subfamilies (and the names are actually consistent in both Linnaean and PhyloCode!):