Born in Dhankuta, Chemjong graduated from the ANFA Academy and joined the Machhindra Football Club. After spending one year at the club Chemjong's impressive performances earned him a move to the Three Star Club in 2007. He has won many tournaments with Three Star Club including the British Gurkha Cup and Aaha Gold CupFootball Tournament. After being the best goalkeeper of south Asia of the time, Kiran was offered by TC Sports Club in January 2017 for two seasons but he signed for a year only. He played his first game for TC Sports Club in February 2017 against the club of Bangladesh and he showed a very impressive performance, helping the club to win the match by 1-0.
Minerva Punjab
On January 23, 2018, he signed a deal with Hero I League club, Minerva Punjab F.C. for an undisclosed amount. He made his debut for the club in an away fixture against NEROCA.He saved a penalty in the 50th minute against Eastbengal which was taken by Katsumi Yusa. He was adjudged as the hero-of-the-match for that fine save. Kiran made total of 8 appearances for the club. He eventually won the 2017-18 I-League with Minerva.
International career
He is currently considered as the First Choice goalkeeper in Nepal. He has a height advantage over more senior keepers like Bikash Malla and Ritesh Thapa. He has produced brilliant displays against oppositions bringing wide acclaims. Chemzong played debut match for Nepal in 2008 AFC Challenge Cup qualifiers held in Phnom Penh, Cambodia, although he broke his jaw in the match. He debuted at the home ground against Afghanistan. In the 2012 Nehru Cup Chemjong won the man of the match award in Nepal's game with India. His performance in the match earned praise from the Indian newspaper The Hindu and from the Maldiveshead coachIstván Urbányi.
Style of play
He is calm with the ball and has quite good reflexes and also good in the air. He does however have a weakness in judging high balls. Chemjong also has a height advantage being 6 ft 1 inches compared to the 5 ft 10 inch average of all players of the Nepali National football team.
Personal life
Nepali players usually earn 50,000 rupees while on international duty and a 10,000 monthly rupee salary while playing for their clubs. In 2015 along with Three Star teammate Bishnu Gurung Chemjong paid a visit to malnourished children in an orphanage in Pokhara saying afterwards that it was a "day to remember".