Justice Chew was born on September 29, 1947 in El Paso, Texas. He received his bachelor's degree from the U.S. Naval Academy in 1971. After serving in the Navy for a few years, he attended the Southern Methodist University School of Law and received his law degree in 1978. At the time of his judicial appointment, he was married and had one son. Justice Chew began his legal career in 1978 as a private practice lawyer in El Paso. He partnered with Paul M. Douglass. They were later joined by Justice Chew's sister, Linda Yee Chew. When she left, his other sister, Patricia B. Chew, took her place. He served on the El Paso City Council from 1989 to 1991 and in 1994, he was elected to the Court of Appeals.