There is plenty of oxygen on the moon
The lunar dust is a major problem for austronauts going to the moon. The dust is very small and with jagged edges that attaches to everything and is very abrashive. It partially wore its way through the outer gloves of the space suits of the first astronauts. The more they tried to brush it away, the more it worked its way into the fabric of the space suits.
The good news is that lunar dust is full of oxygen just laying around:
An early, persistent problem noted by Apollo astronauts on the Moon was dust. It got everywhere, including into their lungs. Oddly enough, that may be where future Moon explorers get their next breath of air: The moon's dusty layer of soil is nearly half oxygen.
The trick is extracting it.
Several teams are working on the challenge and they are already able to extract half of the oxygen from the lunar dust.
NASA and the Florida Space Research Institute, through NASA's Centennial Challenge, are sponsoring MoonROx, the Moon Regolith Oxygen competition. A $250,000 prize goes to the team that can extract 5 kg of breathable oxygen from JSC-1 lunar simulant in just 8 hours.
The competition closes June 1, 2008, but the challenge of living on other planets will last for generations.