Born in Bedford, Virginia in 1929, Chambers was the third of five children raised by his mother, Charlotte Chambers (including his brother Andrew, who later became a Lieutenant General in the U.S. Army). After Chambers' father died, his mother began working in the War Department to support the family.

Chambers served in Junior ROTC while attending Dunbar High School in Washington, D.C. After graduating as class valedictorian and commander of the corps of cadets, Chambers considered using the college/university level ROTC program to also pay for college. However, Wesley A. Brown, the first African American graduate of the U.S. Naval Academy, encouraged him to apply there. Chambers did and became the second African American to graduate from the Naval Academy on June 6, 1952.

In 1954, after 18 months of FLIGHT training, Chambers was designated as a Naval Aviator. His first fleet assignment was to an air-antisubmarine warfare squadron, VS-37, where he flew the Grumman AF Guardian. Transitioning to the light attack community, he later flew the A-1 Skyraider with VA-215 and then, following postgraduate education, transitioned to jet light attack aircraft, flying the A-4 Skyhawk with VA-125 and VA-22. He then established VA-67 (later VA-15) as its first commanding officer, flying the A-7 Corsair II.

From 1968 to 1971, Chambers flew combat missions over Vietnam from USS Ranger and USS Oriskany. In 1972 he was promoted to captain and placed in command of the USS White Plains, a combat stores ship.

In April 1975, while in command of the aircraft carrier USS Midway, Chambers was ordered to "make best speed" to the waters off South Vietnam as North Vietnam overran the country to take part in Operation Frequent Wind, the evacuation of U.S. and South Vietnamese personnel. At the time the carrier was in Subic Bay Naval Base with the engineering plant partially torn apart.

After consultation with the USS Midway Carrier Task Force CO, Admiral william L. Harris, Chambers issued the order to allow the plane to land on the Midway's FLIGHT deck. The arresting wires were then removed, all helicopters that could not be safely or quickly relocated were pushed over the side and into the sea. To get the job done he called for volunteers, and soon every available Sailor was on deck, regardless of rate or duty, to provide the manpower to get the job done. An estimated US$10 million worth of UH-1 Huey helicopters were pushed overboard into the South China Sea. With a 500-foot ceiling, five miles' visibility, light rain, and 15 knots of surface wind, Chambers ordered the ship to make 25 knots into the wind. Warnings about the dangerous downdrafts created behind a steaming carrier were transmitted blind in both Vietnamese and English. To make matters worse, five additional UH-1s landed and cluttered up the deck. Without hesitation, Chambers ordered them scuttled as well. Captain Chambers recalled in an article in the Fall 1993 issue of the national Museum of Aviation History's Foundation magazine that:

After retiring from the Navy, Chambers became Director of program development at System Development Corporation. In 2010, Chambers took part in commemorations honoring Operation Frequent Wind.

On that same day, South Vietnamese air force major Buang-Ly loaded his wife and five children into a two-seat Cessna O-1 Bird Dog and took off from Con Son Island. After evading enemy ground fire Major Buang headed out to sea and spotted the Midway. The Midway's crew attempted to contact the aircraft on emergency frequencies but the pilot continued to circle overhead with his landing Lights turned on. When a spotter reported that there were at least four people in the two-place aircraft, all thoughts of forcing the pilot to ditch alongside were abandoned—it was unlikely the passengers of the overloaded Bird Dog could survive the ditching and safely escape before the plane sank. After three tries, Major Buang managed to drop a note from a low pass over the deck: "Can you move the helicopter to the other side, I can land on your runway, I can fly for one hour more, we have enough time to move. Please rescue me! Major Buang, wife and 5 child."

On April 29, 2015, Chambers traveled to San Diego, California to speak aboard USS Midway, now a museum ship open to the public, in commemoration of the 40th anniversary of Operation Frequent Wind.