Is it "Chinese simplified", or "simplified Chinese"?
"Simplified Chinese" is the normal way to describe this. But as far as I know, it refers to the system of writing, not the language. Hence it is "Simplified Chinese characters" (link to Wikipedia article).
I've studied Mandarin for years and all references I've come across, from course titles to textbooks have been to simplified Chinese. Incidentally, I wish that I'd had the option to study traditional Chinese at a local university.