Chester Dupree is Bernice Hibbert's brother, Julius Hibbert's brother-in-law and the Hibbert children's uncle.
Chester is a unique character because Simpsons fans saw what he looked like the first time in the mobile game Simpsons: Tapped Out. 
He is unemployed and owes money to Dr. Hibbert. Bernice told Dr. Hibbert to loan money for Chester, so that he could build his shed. Dr. Hibbert said that he was never going to finish it.
Chesters Official Image, and tapped out image.
Dr. Hibbert and Bernice talking about Chester/ Origin of Chester