Chun's acting career began in 1983 when he auditioned at Munhwa Broadcasting Corporation and was selected. His first roles were mostly in miniseries and one-off telemovies. He came to prominence with viewers in the long-running KBS drama Love on a Jujube Tree, which garnered him the Baeksang Arts Awards for Best New Actor in the television category in 1992. In later years, he earned the sobriquet "the national father" after portraying the father of the main characters in the family dramas My Golden Life and Once Again, both of which had viewership ratings of over 30%. His portrayal of a bankrupt and down-on-his-luck man who has a complex relationship with his wife and their four adult children in My Golden Life won critical acclaim from both critics and viewers and earned him the Grand Prize at the 2017 KBS Drama Awards and a string of award nominations.