He graduated with a BSc in Mechanical Engineering (upper second class honours) from the University of the West Indies in 1980. He worked as an engineer at Trintoplan Consultants Limited in Trinidad and at Schlumberger in Libya.
Archie then studied law at the Solent University in Southampton, England, receiving his LLB in 1984. He received his Legal Education Certificate at Hugh Wooding Law School in St Augustine. He was admitted to the Bar of Trinidad and Tobago in 1986. Archie worked initially for Clarke and Company. He then served as State Counsel and Senior Crown Counsel for the governments of Trinidad and Tobago, the Turks and Caicos Islands and the Cayman Islands. He was Solicitor General of the Cayman Islands and acted on occasion as the Attorney General.
On March 1, 1998, he was appointed a puisine judge of the Supreme Court of Judicature. He became a Justice of Appeal on April 2, 2004 and chief justice on January 24, 2008. He is the eighth chief justice of Trinidad and Tobago and the youngest person to have taken the role. He is Chairman of the Judicial and Legal Services Commission, President of the Trinidad and Tobago Judicial Education Institute, and a fellow of the Board of the Commonwealth Judicial Education Institute. In 2013, he received the Order of the Republic of Trinidad and Tobago.
- "The Judiciary of Trinidad and Tobago : About the Judiciary : The Chief Justice". Ttlawcourts.org. Retrieved 13 December 2017.
- "Middle Temple". Middletemple.org.uk. Retrieved 13 December 2017.
- "A favour for CJ's friend?". Trinidadexpress.com. 11 November 2017. Retrieved 13 December 2017.
- "Invasion of privacy". The Trinidad Guardian Newspaper. Retrieved 13 December 2017.
- "Archived copy". Archived from the original on 2017-12-14. Retrieved 2017-12-13.CS1 maint: archived copy as title (link)
- "Judge writes judges on CJ Archie - Trinidad and Tobago Newsday". Newsday.co.tt. 18 November 2017. Retrieved 13 December 2017.