We are "tantalisingly close" to seeing commercial space travel, according to Richard Branson.
The entrepreneur said that a recent test flight had put the company "back on track".
It was the first successful flight since a horrifying crash four years ago, which some worried could undo the company's attempt to sell people trips to space.
The spacecraft was carried to an altitude of 46,500ft (14,173.2m) by its mother ship before being released over the Mojave Desert in California, USA, on Thursday.
Virgin Galactic said the spacecraft achieved supersonic speed before gliding back down to the ground.
It was the firm's first powered flight since its original spaceship crashed in 2014, killing one pilot.
Unity has previously flown on test flights in which it glided without lighting the rocket.
Virgin Galactic founder Sir Richard tweeted: "virgingalactic back on track. Successful powered flight, Mach 1.6. Data review to come, then on to the next flight. Space feels tantalisingly close now."
The space tourism company said in a statement: "The flight has generated valuable data on flight, motor and vehicle performance which our engineers will be reviewing.
"It also marks a key moment for the test flight programme, entering now the exciting phase of powered flight and the expansion to full duration rocket burns.
"While we celebrate that achievement, the team remains focused on the challenging tasks which still lie ahead."
Additional reporting by Press Association
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