An angry Chao told the protesters to "leave him alone" as she tried to walk to the other side of the vehicle with the help of security guards.
"No, he's not" separating families, she said. "You leave my husband alone," she added, pointing at the group.
"How does he sleep at night? How does he sleep at night?" one protester said.
The encounter was caught on video and posted to Twitter by a user with the handle @Roberto62543651. He identified himself and the other protesters as Georgetown students.
The video had been viewed more than 200,000 times in two hours today.
Another observer caught the episode on camera and posted it to Twitter:
"A group of protesters confronts Mitch McConnell and Elaine Chao with @ProPublica's audio of children separated from their families at the border while leaving a @Georgetownevent." - Jesus Rodriguez (@jesusrodriguezb) June 26, 2018
Chao's office did not immediately respond to a request for comment. A spokesman for McConnell declined to comment.
Chao and McConnell are not the only Republican officials who have been confronted over the separation of migrant families at the border.
Homeland Security Secretary Kirstjen Nielsen faced protesters when she dined at a Mexican restaurant last week; White House press secretary Sarah Huckabee Sanders was asked to leave a restaurant in Lexington, Virginia, over the weekend; and protesters gathered outside the apartment of Trump adviser Stephen Miller.
