Insofar as I'm aware, he's with the Mariners organization. During the UVA–Cal State Fullerton game today, the ESPN2 "Bottom Line" ticker kept listing notable baseball alumni from both schools, and "Nationals P Chad Cordero" was one of the names.
I assume this is just sloppiness by someone at ESPN, but I can't help but asking whether something changed and he's somehow back with the Nationals organization.