The visit was part of QBE Team Talk, an initiative which sees top Aviva Premiership Rugby players visit QBE offices around the country.
The Tigers and England front-rowers were joined by employees of QBE, Official Business Insurance Partner of Premiership Rugby, for the quiz, which was hosted by television and radio presenter John Inverdale.
Cole and quiz teammates Jason Cowlishaw and Simon Whittaker came out on top and took home the champagne.
Chuter and Cole also answered a series of questions submitted by QBE staff. A prize of four tickets to a Premiership Rugby match was awarded to Elisabeth Martin, after the players selected hers as the best question submitted on the day.
Cole said: “It has been a great afternoon with the QBE Stafford office taking part in the Question of Sport quiz. There was definitely a competitive spirit between the two teams which was good to see.”
Mike Bowen, commercial manager, added: “QBE Team Talk really has created excitement in the Stafford office. To have international rugby players here to meet our employees and share their experiences has given us a great insight into the lives of professional sportsmen.”