The campus hot-dog stand sells tofu wieners. A recent pro-marijuana rally drew a crowd of 10,000, roughly a third the size of the student body. And according to one professor’s analysis of voter registration, the 800-strong faculty includes just 32 Republicans.

Chancellor G.P. “Bud” Peterson surveys this landscape with unease. A college that champions diversity, he believes, must think beyond courses in gay literature, Chicano studies and feminist theory. “We should also talk about intellectual diversity,” he says. So over the next year, Mr. Peterson plans to raise $9 million to create an endowed chair for what is thought to be the nation’s first Professor of Conservative Thought and Policy.

Mr. Peterson’s quest has been greeted with protests from some faculty and students, who say the move is too — well, radical. “Why set aside ...