Beyoncé and Jay-Z arrived at Scarsdale Village Hall shortly after it opened at 9 a.m on Tuesday to get their marriage license. "It was just the two of them," an eyewitness tells PEOPLE. "They were very polite and smiling as they filled out the paperwork. They were holding hands for a while. They looked really happy."

Could their happiness be because the longtime couple is finally putting the constant wedding and split rumors to rest? Although a rep for Beyoncé, 26, had no comment and a rep for Jay-Z, 38, could not be reached, the courthouse trip is the first real indication that the pair – who first started dating in 2002 – will walk down the aisle.