The 43-year-old actor had never been more star-struck than when he got close to the "Ziggy Stardust" hitmaker - who died of cancer in 2016 - but he couldn't bear the idea of how "mortifying" it would be to look back on the encounter if he said something silly.
He told Empire magazine, "I was probably most star-struck when I was living in New York, maybe 16 years ago. On Spring Street and Lafayette, there's a magazine shop. It's not there anymore."
"I went in, looking at some magazines - and David Bowie walked in. Stood right next to me."
"I remember being very star-struck but I actually ended up with this internal dialogue where I thought, 'Put back the magazine and walk out. Don't mess it up.' "
"So that's what I did! I knew the memory would be mortifying if it went wrong. But fabulous if nothing happened."
"It was better that nothing happened than to mess it up somehow."
Meanwhile, Chiwetel believes his most famous friend is Don Cheadle.
Asked who the most famous person he could text right now is, he said, "You mean, who is the most famous person in my phone? Or who would actually be happy to receive a text from me?"
"These are two different things. The most famous person that I text frequently, I would say, is probably Don Cheadle."
The "Doctor Strange" actor admitted he has "danced on the line" of doing things that aren't legal.
Asked if he's ever knowingly broken the law, he said, "I mean, depends on what kind of laws we're talking about!"
"I may have danced on the line."
"But I don't think I've ever knowingly broken any serious law. Any law that should be in place, anyway."