In order to evolve your units you must first go through an evolution quest. Each quest, like one from the story areas, takes a certain amount of stamina and you are required to bring a friend/support. Upon completing the quest you receive exp, coins and your unit will evolve. The quest you undertake depends on the amount of stars the unit undergoing evolution has.

Completing the fifth quest on the evolution temples automatically gives you a chip, regardless of whether or not you completed the previous four.

List of Evolution Temples