Olson completed the 5,000 meter course in 18 minutes, 20 seconds.
Mount Rainer sophomore Jordan McPhee won the title with a phenomenal performance of 17:24. Union freshman Alexis Fuller finished second at 18:07.
“Chandler ran beautifully,” Woodinville coach Sandy Laurence said.
“She raced like a champion and I’m really proud of her. It was a very exceptional race for being so sick.”
Olson’s third-place finish was a repeat of last year’s, when she was also under the weather. Inglemoor’s Kyra Burke, a junior, finished 17th with a time of 18:53.