Q. Browsing both the 15th and 16th editions for citation rules, I don’t see instruction on how to cite live performance. Given that performance studies, dance/theater criticism, and musicology/ethnomusicology are established disciplines, and that observing live performance is a necessary research method, I don’t see why that source (and its creators/producers) should not be cited.
A. It’s not that Chicago rejects live performance as a legitimate source; there simply isn’t room for examples of every kind. If live performances are the backbone of your research, the lack of a citation form in CMOS should not prevent you from citing them. You can mimic the standard order of citation elements (performer, title, place, date) or order them in a way that makes sense for your work, such as chronologically for works by the same person.
[Update: CMOS now covers how to cite live performances. See the 17th edition, paragraphs 14.266 and 15.57.]