Bigelow's first feature since her 2010 'Best Picture' winner The Hurt Locker chronicles the decade-long special operations forces mission to capture Osama Bin Laden.
"I think with any movie when you're telling a story like we're telling, there's an insane amount of pressure," Chastain told The Hollywood Reporter, "because you want to honour the people that really were there, and you want to honour history.
"And you don't want to tell the wrong story."
Chastain went on to explain that the film's shooting location in India, where it drew protests from Hindu activists who objected to it being used to depict Pakistan, had contributed to the pressure.
"We shot a lot of Chandigarh, India, which is near the border of Pakistan, and it was a long shoot, it was a lot of stress.
"But I will say it was one of the best scripts I've ever read, the part is phenomenal, and the company that I'm in that film, it's wonderful."
Zero Dark Thirty stars Chastain, Joel Edgerton, Jennifer Ehle, Chris Pratt and Mark Duplass, and is penned by The Hurt Locker scribe Mark Boal.
The film is set for release on December 19 in the US, with a UK release date yet to be set. Watch the trailer below: