Q. What should I do if I am citing a newspaper article in Chicago style and the article does not have an author?

According to the Chicago Manual of Style, 17th edition, section 14.191, you should format newspaper citations. 

Basic format for a Newspaper citation:

Author, "Title of Article," Title of Newspaper [in Italics], date. URL or database name (if available).

If there is no author for an article, you should begin the citation with the title of the article.

Examples:

Jasper Summy, "Western to Offer Women’s Entrepreneurial Leadership Certificate," The Front, July 28, 2021, https://www.westernfrontonline.com/article/2021/07/certificate-in-womens-leadership?ct=content_open&cv=cbox_latest.

“Up, Up, and Away,” Oregonian, September 15, 2016.