Hector had a strong first run and is just two hundredths of a second ahead of Valerie Grenier of Canada.
Meanwhile, Mikaela Shiffrin is being chased by Sundsvall-born German Emma Aicher in the fight for the overall World Cup title. Aicher needs a victory to have a chance of passing Shiffrin - and after the first run the drama remains alive.
Aicher is third, 26 hundredths of a second behind the leader. Shiffrin didn't get going and is only in 17th place, more than a second and a half behind the leader.
The second run starts at 12:30.
