It's "betting on something or someone, having confidence." It takes figuratively to put chips to a number on the roulette wheel, because we believe it is the winner. Although not as common, you can also interpret 'chips' as fichines to play in pinball, table football or other entertainments for time, and then it would be "to smote or feed a situation for it to continue, to progress; good or bad, which can be compared to "warm the head".
