Born in Long Beach, California, Chandler was raised in Whittier and graduated from Whittier High School in 1967. He was considered one of the best all-around high school athletes to play in southern California. He was All-CIF in football and basketball and was one of the country's top high school decathletes, high-jumping 6 ft 7 in (2.01 m), pole-vaulted more than 13 feet (4.0 m), and put the 12-pound (5.4 kg) shot 57 feet (17 m).
Chandler played college football at the University of Southern California in Los Angeles; he was a captain and the team's leading receiver during his senior year in 1970. He played in two Rose Bowl games; as a junior he was named Most Valuable Player of the 1970 Rose Bowl. In the third quarter, Chandler caught a 33-yard touchdown pass from Trojan quarterback Jimmy Jones and broke several Michigan tackles to score and gave USC its margin of victory, 10–3.
A seventh round pick in the 1971 NFL Draft, Chandler played nine seasons with the Buffalo Bills (1971–1979) and three with the Oakland Raiders (1980–1982). He led the NFL in receptions from 1975–1977 with 176, and was named Second-Team All-Pro in 1975 and 1977. He also caught four passes for 77 yards in the Raiders' 27–10 Super Bowl XV victory over the Philadelphia Eagles in January 1981.
In the first game of the 1981 season against the Denver Broncos, Chandler stretched out for a pass and took a hit so severely it ruptured his spleen. Chandler was rushed to a Denver hospital where doctors saved his life. Chandler made a miraculous recovery and returned to the field later in the season, appearing in a total of eleven regular season games.
He retired in July 1983; for his career, he had 370 receptions for 5,243 yards and 48 touchdowns, along with 11 carries for 18 yards.
Chandler and running back O.J. Simpson were teammates for a season in college (1968) and seven in the pros at Buffalo (1971–77).
Chandler served as a color analyst for NFL games on NBC in 1983, hosted 2 On The Town for KCBS-TV in Los Angeles from 1984–1987, was a sports reporter for KABC-TV in the late 1980s and hosted Amazing Games (a global documentary series about the world's most exotic sports) for ESPN in 1989. He also served as a "Technical Advisor" for the humor book The Unofficial NFL Players Handbook.
Chandler's father Gene was the mayor of Whittier in 1987–1988. Chandler eventually married his college sweetheart Marilyn and had three children: Marisa, Justin, and Emma. Chandler earned a law degree from Western State University College of Law.
A non-smoker, Chandler began experiencing a nagging cough in 1994. A rare strain of lung cancer was discovered in his lungs in September 1994. He continued to work on Raider broadcasts while undergoing chemotherapy treatment at the USC Norris Cancer Center, but died there on Friday, January 27, 1995, at the age of 45, after a four-month battle with cancer. He was buried at Rose Hills Memorial Park in Whittier.
In 1996, USC established the annual Bob Chandler Award, given to an underclassman based on his athletic ability, academic scholarship as well as character on and off the field. The award funds a scholarship for the player's full tuition, room and board for the following year.
Chandler was inducted into the USC Hall of Fame in November 1999. Highlights of his USC athletic career are on permanent display in USC's Heritage Hall lobby.