The emotional scene played out at the Forbes Power Women's Summit in New York City ... after the Team USA gymnast was asked to open up about the Paris Games controversy for the first time since it all went down.

She had to pause for several seconds to collect herself before she get her words out ... and when she ultimately answered the questions -- she said she felt like she had lost a part of her when officials took her bronze away.

"The biggest thing that was taken from me," she said, "was the recognition of who I was."

"Not just my sport, but the person that I am. To me, everything that has gone on is not about the medal. It's about my skin color, it's about the fact that there were things that have led up to this position of being an athlete."

Chiles was first given the honor on Aug. 5 in Paris ... after a review of her floor score bumped her above Romanian athlete Ana Barbosu for third place. A short time later, though, officials ruled Team USA had missed the deadline to appeal the judge's decision ... and the accolade was then given to Barbosu.

Ensuing attempts to get Chiles her bronze back have been unsuccessful, and clearly, it's weighing on Chiles -- who compared the whole saga to a dark chapter in her life where she was abused by one of her coaches.

"I felt like when I was back in 2018, where I did lose the love for the sport, I lost it again," she said. "I just felt like there wasn't a lot of people supporting me who I thought that could support me in that situation."

"I felt like I was really left in the dark."

Despite the controversy, Chiles was still able to bring home the gold medal in the team event.