Chao is also the wife of Republican Senate Minority Leader Mitch McConnell (Ky.), but she worked as the secretary of transportation until she resigned in January.
"Who else is staying far away from Kroger, Fred Meyer, and any of their other stores since they've added corrupt Elaine Chao to the board?" tweeted the account for a Democratic Super PAC.
Kroger is based out of Cincinnati, Ohio, and is the parent company of many other stores including Food 4 Less, Dillons, Fred Meyer, King Soopers, Pay-Less Super Markets, City Market, and Foods Co.
On Wednesday, social media users circulated a list of companies to boycott in protest.
"Hey @kroger, I've shopped at your stores for 20+ years — but no more! Get #ElaineChao TF off your board. Now!" claimed body language expert Jack Brown.
"Kroger's choices in executives should reflect its company values. Its leaders need to decide if blatant corruption is one of those values," said another social media user.
"Loyal Michigan Kroger shopper here. NO WAY will I EVER shop Kroger with Elaine Chao on your board!!! I am so sad, I have LOVED Kroger. So disappointing!!!" said another.
"F*** Kroger for adding Elaine Chao to Board of Directors. Y'all remember Elaine Chao. Mitch McConnell's wife aka Mrs. Turtle whose only accomplishment as Trump Transportation Secretary was transporting our taxpayer dollars to her bank account," read another tweet.
Chao was the first Asian American woman to be nominated to a U.S. president's Cabinet when she was nominated to be secretary of labor by former President George W. Bush in 2001. She resigned her office in the waning days of the Trump administration after the Jan. 6 riot at the U.S. Capitol.
Here's a profile of Elaine Chao:
Elaine Chao: From immigrant roots to a president's c... www.youtube.com