Neither Elon Musk's company nor Blue Origin have done it just yet, and it's a long time coming for Richard Branson's space tourism venture.

For 14 years, Richard Branson and Virgin Galactic have been working toward taking people to space, and they may be about to beat Elon Musk's SpaceX and Jeff Bezos' Blue Origin to the milestone. 

The aspiring space tourism outfit says it could conduct the fourth test flight of its SpaceShipTwo space plane as soon as Thursday from the Mojave Air and Space Port in California. The exact time the launch window opens has not been announced, but based on airspace closures listed by the Federal Aviation Administration, it will need to happen in the morning between 7 a.m. and noon PT.

The test flight will see Virgin Galactic's huge carrier airplane take off from Mojave carrying VSS Unity (an individual unit of SpaceShipTwo, titled the way each individual Space Shuttle had its own name). Unity will then detach and fire its rockets a few seconds later, shooting itself as high as 50 miles (80 kilometers) above the surface.

Technically that's in the mesosphere, below the widely accepted boundary of space at 62 miles (100 kilometers) above the Earth's surface. But such definitions can be a little loose, and the company says its pilots will likely feel like they're in space.