Complex sentence: The Second City was the first on-going improvisational theater troupe in the United States, choosing its self-mocking name from the title of an article about Chicago by A. J. Liebling that appeared in "The New Yorker" in 1952.
Split into simpler sentences: The Second City was the first on-going improvisational theater troupe in the United States. The troupe chose the self-mocking name from the title of an article about Chicago by A. J. Liebling that appeared in "The New Yorker" in 1952.