The Olympic champion in the discipline produced a conservative first run on a course softened by mild weather conditions, finishing fourth quickest, 0.44 seconds behind halfway leader Viktoria Rebensburg of Germany.
Watch: Shiffrin’s first run in Giant Slalom
Rebensburg, giant slalom gold medallist at the Vancouver Olympics in 2010, will take a 0.19 second lead over Slovakia's Petra Vlhova into the second run later on Thursday.
Rebensburg leads Giant Slalom after first run in Are
Norway's Ragnhild Mowinckel was third fastest, 0.37 slower than 29-year-old Rebensburg.
"The wind was not ideal," Shiffrin, who won gold in the Super-G to continue a stunning season, said at the finish.
It's always full gas in the second run and I will see where I can maybe take some more risks.
Reigning world champion Tessa Worley of France will need to make up 0.73 seconds, having gone fifth quickest.
The top 30 begin their second runs in reverse order at 1645 GMT.