Capitalization in Titles of Works
Q. The “Life Style” section of a newspaper is referred to in dialogue. The dialogue is in double quotations. Should the name of the newspaper section also have a set of double quotation marks? I searched for an answer or a reliable example and could find none.
A. Chicago style leaves the titles of newspaper sections unquoted, which solves your problem. But in general, use single quotes for a quote within a quote. CMOS 13.28, 14.202, and 14.205 have the examples you’re looking for.