As a result, an outstanding performance by Armstrong, who excelled at the discipline before his retirement in 2005, will catapult the 37-year-old American into the top three again.
When the stage began, the fourth-place Armstrong trailed second-place Andy Schleck by 1 minute 29 seconds and Frank Schleck by 30 seconds.
Armstrong will have to make up lots of time on the Schlecks ahead of Saturday's stage and the long, punishing ride up the Mont Ventoux, where the final standings will be decided.
The Schlecks proved in Wednesday's stage that they can outclimb the American and Wiggins.
But Contador has shown that he is untouchable in the mountains and, barring accident or illness, looks to have his second Tour title locked up.
The 158 riders left in the race ride the time trial in inverse order of their place in the standings. The first rider on the course, Hutarovich, trailed Contador, who is to ride last, by more than 3 hours.
The Tour ends Sunday in Paris.