Shiffrin fourth in first run of Czech giant slalom race
The over World Cup leader trailed 0.43 seconds behind Olympic giant slalom champion Hector, who clocked the fastest time to edge Switzerland's Camille Rast by just 0.2 seconds.
Austria's Julia Scheib, the World Cup leader in the discipline, trails at 0.26 seconds behind the leader in third.
Some of the top-ranked skiers skipped the event in the Czech Republic, including Italy's Sofia Goggia and Federica Brignone, two weeks before the Milan-Cortina Olympics get underway.
The second run is scheduled for 1230 GMT.