The couple were married for nine years, but split in 1994. They are the parents to one daughter, 25-year-old Alexa Ray.
Joel reportedly wrote his hit 'Uptown Girl' about Brinkley while the pair were dating.
The supermodel told Access Hollywood Live host Billy Bush that the 'We Didn't Start The Fire' singer stressed the importance of delivering her lines at the proper volume.
"The second he heard that I was doing this he said, 'Make sure you get lessons to project your voice because you've really got to get it to the back of the room'," Brinkley said. "So, yeah, I've been taking singing lessons and dancing lessons."
In spite of the demanding schedule required for starring in a Broadway production, the star insisted that appearing in Chicago has been a career highlight.
"I'm having such a great time… [Roxie] is so much fun to play," she said. "I do eight shows a week. It is so much fun! I'm loving this adventure in life."
While Brinkley is primarily known for her modelling, she also has extensive acting experience, including a recurring role in the National Lampoon's Vacation film series as a mysterious woman who seductively haunts Chevy Chase's Griswald family patriarch.
Her 11-week run in Chicago wraps up on June 19.
> Brinkley gave daughter "tough love"
Watch Christie Brinkley discuss Chicago below: