Muller, however, took another step towards securing the 2013 Drivers’ Championship when he qualified in second place.
The Frenchman has a mathematical opportunity to take his fourth WTCC crown on Sunday, while Honda could also wrap up the Manufacturers’ title.
“It's not easy beating Yvan - I think everyone knows that he'll be a four-time World Champion this year - but it's fantastic to get my first pole position in World Touring Cars,” said Chilton, who posted a best finish of 12th in Sonoma last year.
“I really love this track. It was quite a scary lap, I could have come off at least three times but I just hung it all together and it was very enjoyable to drive and a great car.”
The Honda Civic of Tiago Monteiro claimed the third spot on the grid, the only car capable of splitting the group of Chevrolet machineries.
Alex MacDowall of bamboo-engineering qualified fifth and best of the Yokohama Trophy, ahead of his team-mate James Nash.
Gabriele Tarquini will start from pole position of the top-10 reverse grid for the second race.