 Despite being ranked as the third-best American swimmer, Neilson participated in the 1972 Summer Olympics in Munich, Germany at the age of 16.In the 100-meter freestyle, Neilson defeated heavy favorites Shane Gould from Australia and her American teammate Shirley Babashoff in an Olympic record time of 58.59 seconds.The victory landed her a spot on the 4×100-meter freestyle relay with Babashoff as well as the 4×100-meter medley relay.