Since opening its original location on West 57th Street three decades ago, Planet Hollywood’s long-term success rate in its home city has proven spotty. But owner Robert Earl hopes the third time will be the charm.

Earl Enterprises, the restaurant chain’s parent company, has signed a lease for 17,500 square feet across four floors at 140 West 42nd Street; the restaurant will occupy the lowest floors of the building.

Planet Hollywood was a hot ticket in the early 1990s, when the likes of Arnold Schwarzenegger and Sylvester Stallone put a public ...