Sometimes, the simplest approach is best. As pluto77 suggests, contact Marriott Rewards customer service and ask them. "Hi. I got the Visa Rewards card and received the bonus points. I've decided that I really don't need the card after all, but I don't want to lose the points. Can you tell me if I can close the Visa now without losing the points?" They'll tell you.
You also may want to consider calling Chase and asking them the same thing. Not because they'll necessarily be the best source for information on this, but the same question might get you a response like, "If we offered you another 25,000 points, would you be interested in keeping the account open?"
I don't know that Chase will react that way, but Amex did that once when I was going to close a Delta Skymiles card. No harm trying!