Chieng is of Chinese descent. He was born in Johor Bahru, Malaysia, and was raised in Singapore and in New Hampshire in the United States. Chieng was educated at Yuhua Primary School, Pioneer Secondary School and Pioneer Junior College in Singapore, and the University of Melbourne in Australia, where he resided at Trinity College and graduated in 2009 with Bachelor of Commerce (Finance) and Bachelor of Laws degrees. He also obtained a Graduate Diploma in Legal Practice from the Australian National University in 2012.
In April 2017, he joined the cast of the Warner Bros. film Crazy Rich Asians directed by Jon M. Chu and starring Constance Wu. The film marks his American feature debut.