The 33-year-old actor was left red-faced when Chastain caught him practicing his moves in his army costume between takes on the movie shoot in the middle of the Jordanian desert.
He explained he had taken up tap in honour of his showgirl mother Dee Dee Wilde, who featured in dance troupe Pan's People on U.K. TV series Top of the Pops.
He tells Britain's Daily Mail newspaper, "I took my tap shoes with me (to the shoot) because I thought I would have lots of time to practise by myself between takes.
"So there I was, tap-dancing away in my full army kit on set, when Jessica came over and asked me what I was doing. I bashfully explained that my mother used to be in a Seventies dance troupe and I was learning to tap-dance.
"All the other guys on set found it really funny. But then she told me all about how she used to be a dancer herself, so in the end I think I had the last laugh."
Corbet Burcher, who plays a Navy Seal in the film, used to be a captain in the Welsh Guards and admits it felt surreal to make a film about the real-life search for terrorist leader Osama bin Laden after serving three tours of duty in Iraq and Afghanistan.
He adds, "To shoot a story about a person who I have personally waged war against was quite strange but absolutely amazing."