However a Southern California woman claims to have one, and was the target of a federal investigation for reportedly trying to sell it.
There is a moon rock on display at the California Science Center in Los Angeles. Weighing less than two grams, it's only about the size of a pebble. Nevertheless, a rock like this is extremely valuable.
"Moon rocks are quite rare," said Ken Phillips from California Science Center. "In fact they are considered the most rare artifacts that NASA allows institutions like ours to have. Our lunar sample was provided by Buzz Aldrin. He was awarded the lunar sample, as were all astronauts, but with the condition that they place them on public display."
A similar rock was actually offered for sale Thursday inside a Lake Elsinore Denny's restaurant. The restaurant was chosen as a meeting place between the seller and the buyer.
But the buyer was actually an undercover NASA agent who took possession of the valuable rock and detained the woman who was trying to sell it.
"I didn't know what was going on," said Lake Elsinore resident Alex Dziedzic who saw the sting operation. "All I saw were the federal cars and the marked cars coming right out of there."
The woman was allegedly trying to sell a moon rock for $1.7 million. NASA says moon rocks are a national treasure and they're not to be sold on any market.
"That's national stuff," said Dziedzic. "That's not right. Nobody but museums and stuff should be in possession of stuff like that."
Over at Jefferson Elementary School in Riverside it was Space Day, where 1600 kids learned more about the universe. Volunteer Floyd Allen wonders if the moon rock was even real.
"It may be something that's just a rock, that's unusual and different, and she's trying to say it's a moon rock," said Allen. "You don't know, I don't know, it would be very difficult to tell."
NASA isn't commenting on the incident or releasing the identity of the female seller. It is unclear if she was arrested or where the moon rock is currently.