In 1935, when she was only fifteen years old, Schou Nilsen set a world record in speed skating when she covered 500m in 49.3 seconds. There were no speed skating events for women at the 1936 Olympic Winter Games (they were not added until 1960), so the 16-year-old Schou Nilsen entered as an Alpine skier.
Her specialty was downhill skiing, but the only Alpine event was the Alpine combined, in which the entrants had to ski a downhill course and a slalom course. Schou Nilsen finished first in the downhill portion of the event, finishing a full four seconds ahead of the other women. But she was only fifth fastest in the slalom and ended up with a bronze medal.
In January 1937, Schou Nilsen set speed skating world records at 500m, 1,000m, 1,500m, 3,000m and 5,000m, each of which lasted for at least twelve years. In fact, her 500m record of 46.4 seconds was not broken until 1955. Schou Nilsen also played on the Norwegian national team in the sport of team handball.