An AAU champion in 400 m at 1956 and in 880 yd (805 m) at 1957 and 1958, Courtney had a memorable duel with Derek Johnson of Great Britain in the 1956 Olympic 800 m final. Johnson took a narrow lead with 40 meters to go, but finally Courtney won by 0.13 seconds, and collapsed with exhaustion. He later wrote:
"It was a new kind of agony for me. My head was exploding, my stomach ripping and even the tips of my fingers ached. The only thing I could think was, 'If I live, I will never run again.'"
The medal ceremony had to be delayed for an hour while he and Johnson recovered. But Courtney did run again. He was the anchorman on the gold medal 4×400 m relay team. He also set a world record of 1:46.8 in the 880 yd (805 m) on May 24, 1957.
Courtney received a bachelor's degree from Fordham University in 1955, and since 1994, the (autographed) varsity jacket from his college track days hangs in a display case along with similar memorabilia from other great Fordham athletes, such as Vince Lombardi.