The child of South Korean immigrants, Chun was raised in the Pacific Northwest and graduated from the Catlin Gabel School in Portland, Oregon.

[1] Chun served as a law clerk for Judge Eugene Allen Wright of the United States Court of Appeals for the Ninth Circuit from 1994 to 1995.

[5] In December 2013, Chun was appointed by Governor Jay Inslee to serve as a Judge of the King County Superior Court.

President Biden nominated Chun to the seat vacated by Judge James Robart, who assumed senior status on June 28, 2016.

[12] On January 3, 2022, his nomination was returned to the President under Rule XXXI, Paragraph 6 of the United States Senate;[12] he was later renominated the same day.