The Chase website gives details for a Marriott Rewards Credit Card (not Premier, which is what most people have). However, when you click the link to apply, it only shows the Premier and the Business cards (both of which have AFs). The rewards structure on the (presumably) no-AF card is 3x at Marriott, 1x everywhere else.https://creditcards.chase.com/marriott/cardmember/rewards_benefits
It looks like there's no way to apply for the no-AF card, at least as a new account. Maybe you can PC to it after a year, if it's a "legacy" card type that Chase keeps open for some customers long after they stop advertising it and close it to new applications.
I'd say your odds aren't good, though. Chase wants their AFs. If people could switch back and forth freely, only paying the AF when they wanted the free night and extra rewards, I think that would expose Chase and Marriott to big losses.