Q. Elsewhere in the Q&A you wrote, “The day I was introduced to the The was the day I learned that irony was finished.” This is just wrong and makes no sense whatsoever. To call The The “the The” is absolutely wrong. Further, The Who should be “The Who.” It’s a proper name, and “the Who” is just wrong. Fix this.
A. Some writers would also prefer The Rolling Stones and The Beatles and The Pointer Sisters—and The Grateful Dead and The Mothers of Invention. And maybe even The University of Chicago Press and The Rock & Roll Hall of Fame. Consistently applied, those look fine, but they’re not Chicago style.
Instead, we treat the definite article as a generic bit of syntax that’s required for some band names and organizations but not for others (Santana, for example). If we extend this logic to the The and the Who, we do so in the spirit of fairness and regardless of official usage—which can be difficult to determine.
But we see your point. Some of the more cleverly nondescript one-word band names risk getting lost outside the context of an album cover without a little help from their editorial friends. So you have our permission to write The The and The Who—and The Band, for that matter. Our rules are not laws. They are meant to be adjusted for the unusual case or to suit a particular context. And that’s The Truth.