Steggall came into the 1998 Winter Olympics in Nagano as one of the medal favourites. Three months earlier, she had become the first Australian woman to win a World Cup event in alpine skiing, after winning the slalom event at Park City, Utah. She posted the fastest time in both of her runs to win by 0.76sec. She then came fifth, sixth and tenth in the next three World Cup events to be ranked sixth in the world. Steggall won a Europa Cup event at Piancavallo. She won Australia's first individual Winter Olympic medal with a bronze in slalom skiing at Nagano in 1998. Her time of 1 m 32.67 s was 0.27 s behind the winner. In December, Steggall placed second in a World Cup event at Mammoth Mountain, missing the gold medal by 0.01 s to Anja Pärson. She had earlier placed seventh at Park City.