On Thursday, February 25, the company will launch its 229-foot-tall Falcon 9 rocket from Cape Canaveral, Fla.
Shortly after launch (and setting loose a new satellite into orbit), the first and biggest part of the rocket will fall back to Earth.
But instead of becoming junk at the bottom of the ocean, the rocket stage will try to land itself on an autonomous drone ship in the Atlantic Ocean.
SpaceX has said it doesn't think this will work, but success has the potential to change spaceflight as we know it.
Here's how it might play out, and what it might mean for the future of the human race.
Kelly Dickerson contributed to this report.