Chee made his political debut in the 2015 general election as part of a five-member PAP team contesting in Bishan–Toa Payoh GRC which won 73.59% of the vote.

Chee was educated at The Chinese High School and Raffles Junior College before graduating from the University of California, Berkeley in 1996 with a Bachelor of Science with highest honours degree in electrical engineering and computer science, as well as a Bachelor of Arts with highest honours degree in economics, under the Overseas Merit Scholarship awarded by the Singapore Government.

[2] He subsequently went on to complete a Master of Business Administration degree at the University of Adelaide in 2006,[3] and was awarded the Newmont Australia Prize for being the Most Outstanding MBA Graduate.

[4] Chee joined the Singapore Administrative Service in 1998 and worked at various Ministries, including Home Affairs, Finance, Transport and Education.

[11] Chee resigned from the Singapore Administrative Service on 11 August 2015 to run for election in the 2015 general election as part of a five-member People's Action Party (PAP) team contesting in Bishan–Toa Payoh GRC after Wong Kan Seng, Hri Kumar and Zainudin Nordin stepped down from their respective wards and politics.

On 9 November 2017, he alleged in a Facebook post that Leon Perera, a Non-constituency Member of Parliament, had made false accusations about Mediacorp making partisan edits on the video of a parliamentary debate on Presidential Elections (Amendment) Bill in February 2017.

[21] In the 2020 general election, Chee contested in Bishan–Toa Payoh GRC as part of a four-member PAP team and they won with 67.26% of the vote against the Singapore People's Party.

Chee was however appointed Senior Minister of State at the Ministry of Finance on 13 June 2022, he was replaced by Desmond Tan at NTUC.

[27] On 18 January 2024, Chee was promoted as full Minister for Transport after resignation of S. Iswaran after the latter was charged for 27 counts related to bribery and corruption.