Odom made the revelation in his forthcoming memoir, Darkness to Light (via People's Natalie Stone). He said USA Basketball had called to inform him an official would be coming by to perform a drug test. He added he had "been smoking weed every day that summer" and thus began panicking about the test.
"We started googling 'fake penises' and studied different ways to beat a drug test," Odom wrote, adding he selected a prosthetic that would arrive the following day.
Odom used urine from his trainer to place in the prosthetic.
"I unzipped my pants and carefully slid the fake penis through the zipper hole," he said. "To get the pee to come out of the tip, I had to squeeze the shaft repeatedly."
The strategy obviously worked because Odom traveled with Team USA to Athens, Greece, for the Olympics. He appeared in eight games, averaging 9.3 points and 5.8 rebounds as the United States collected a bronze medal.