Palin, the Republican vice-presidential nominee in the 2008 election, last week tweeted a picture of herself and her husband, Todd, visiting a Texas location of the restaurant. The photo was accompanied by the message, "Stopped by Chick-fil-A in the Woodlands to support a great business."
The restaurant chain has come under fire recently because its owners vocally oppose same-sex marriage.
"The music selection was a poor choice and was not intended to be linked to any news story," a CNN representative told The Hollywood Reporter Monday. "We regret any perception that they were planned together."