Nasa is offering a $250,000 prize to the first scientists who can extract breathable air from moondust.
The agency wants to provide oxygen on tap for future colonies of astronauts living in moonbases.
The winner of the contest will have to produce 5kg (11lb) of oxygen from simulated lunar soil in just eight hours.
Apollo astronauts found the Moon to be covered with dust when they flew there between 1969 and 1972.
The dust is 43 per cent made up of oxygen but it is trapped in the form of materials called oxides.
The most common is silicon dioxide but oxides of calcium, iron and magnesium are also plentiful.
Eric Cardiff, of Nasa’s Goddard Space Flight Centre, near Washington, is leading a team trying to get at the gas.
He says the secret is to vapourise the moondust. He said: “It’s a simple aspect of chemistry. Any material crumbles into atoms if made hot enough.”
Cardiff’s team has already produced small amounts of oxygen from a mixture of basalt and glass that resembles the surface of the Moon.
Nasa’s contest is called MoonROx, the Moon Regolith Oxygen competition. You have got until June 1, 2008, if you want to have a go.
Last week, chief Nasa scientist Alan Stern suggested bombing the Moon with ice to provide essential water for lunar colonies.
The photo shows Apollo 17 astronaut Harrison Schmitt examining a lunar boulder.