And in Sochi, at her fourth Winter Games, Randall has a real chance to finally get one: she is entering the individual freestyle sprint as one of the big gold-medal favorites, another status previously unheard of for an American.
"The Olympics are really kind of the gold standard in the sport," Randall said in a phone interview. "It's been wonderful to achieve the success I have had in the sport, but success at the Olympics is really the final one to go for. I feel my career has been building up to this point. I know it's just one race on one day, but I would love to add an Olympic medal to that collection."
In the wake of Randall's successes, a number of other American skiers have also emerged on the World Cup. On the men's side, Simi Hamilton won a sprint stage on the Tour de Ski this season, while veteran Andrew Newell is also an outside contender in the men's sprint.
But Randall is the team's only real star.
"We have a unique opportunity to make history in Sochi," U.S. cross-country head coach Chris Grover said when the American team was announced. Only one American has ever won an Olympic medal in cross-country skiing, with Bill Koch taking silver in the men's 30-kilometer race at the 1976 Innsbruck Games. On the women's side, Randall is the only one to even make the top 10, with an eighth-place finish in the classical-style sprint in Vancouver four years ago as her best result.
This time, though, the individual sprint is a freestyle event by far Randall's best discipline. At the age of 31, she is also a much stronger skier than four years ago. Nine of her 10 individual World Cup victories have come since 2011, and all of them in freestyle sprints the event she specializes in. She won the last two World Cup events before Sochi, in Poland and the Czech Republic, although those victories came against slightly weakened fields as some top skiers focused on training for Sochi.