Gender discrimination in public accomodations - is this even legal?

Hotel Reservation: Floor For Women Only - Travel News Story - WKMG Orlando:

"A lounge at the hotel also will be reserved for women only when the hotel opens in September."

This comes from the announcement of a new Marriott hotel to open later this year in Grand Rapids. No doubt the company's legion of high-priced lawyers has gone over this, but I find it hard to believe that this does not amount to impermissible gender discrimination in public accomodations. Could a hotel get away with having a men-only floor or a lounge reserved only for men? I don't think so.