In the final on October 17, she set a personal best of 52.2 seconds but narrowly missed out on becoming the first British female to win a track gold, as Australian legend Betty Cuthbert won in an Olympic record time.
So, what is Packer doing on this list?
Her big achievement came three days later in an event she had not even expected to be running.
Before 1964, Packer had never competed over 800m, and only took it up to improve her endurance in her specialist event.
After her silver in the 400m, she considered dropping out of the half-mile and planned a shopping trip instead - but she was driven on by her team-mate Mary Rand winning long jump gold, and by her fiancé Robbie Brightwell's disappointing fourth place in the men's 400m.
Packer qualified slowest for the final, but in only her eighth competitive 800m race she stayed with France's Maryvonne Dupureur before kicking for home with an extraordinary burst of pace.
Packer not only won the race, but did so with a new world record of 2:01.1. She immediately retired, aged 22.
She and Brightwell's sons, Ian and David Brightwell, became professional footballers and both played for Manchester City.