All the other information says Trinity UCC is a totally independent entity. Now that doesn't mean someone in that crazy bunch over at UCC isn't going to claim them, but it's enough to suggest TUCC doesn't claim UCC, which actually would be a good thing. GO TUCC, GO.
Origins: It is true that Illinois senator (and Democratic presidential hopeful) Barack Obama has been associated with Chicago's Trinity United Church of Christ (a single church which is part of the United Church of Christ denomination) for about twenty years, and it is true that TUCC describes its congregation as "an African people" who remain "true to our native land."