"I hereby challenge Gov. Christie to a three-mile race, a push-up contest and a chin-up contest. Whatever he wants to bet, I have no doubt of the outcome," Brown said.
Christie's weight problem has dogged him in office. He opened up about it in a July interview with ABC News, calling obesity "a really difficult thing to deal with."
"My blood pressure’s fine, my cholesterol is fine," Christie said. "I’m in good physical shape in terms of those indicators. But I have to lose weight and I get it."
Christie was a highly anticipated speaker at last week's convention, where he took several opportunities to blast California for its fiscal problems.
"I cannot believe you people elected Jerry Brown over Meg Whitman," Christie told the convention delegation from California, according to the Los Angeles Times. "Jerry Brown? I mean, he won the New Jersey presidential primary over Jimmy Carter when I was 14 years old."
Brown ran unsuccessfully for the Democratic presidential nomination several times in the 1970s, 80s and 90s.
In 2010, he defeated former eBay president Meg Whitman to become governor for the second time. His first term ran from 1975 to 1983.