Chung Woon started playing football at Hakseong Elementary School, close to the Ulsan Hyundai, going on to the Hyundai Middle and High schools, before going to Myongji University in Seoul.

[1] His career at his hometown club only lasted during the 2012 season, being unable to secure a single first team cap.

[citation needed] He went to Croatia in early 2013 and passed a trial with the Prva HNL team Istra 1961 from Pula, signing a two-and-a-half-year contract.

[citation needed] He made what was both his first-team and professional debut on 23 February 2013 in a goalless away draw with Osijek, coming for Adnan Aganović in the 67th minute, and scored his first goal in another away match against the same team, on 18 August 2013, scoring his team's third goal in a 3–1 win.

[citation needed] After two years with Istra 1961, Woon moved to RNK Split, along with his teammate Slavko Blagojević, signing a three-and-a-half-year contract.