Clint Eastwood's upcoming war biopic follows the experiences of Kyle as he becomes a battlefield legend for his lethal accuracy in Iraq, only to return home to his wife and children four years of duty later with post-traumatic stress disorder.
Asked by an offscreen journalist how he feels about his 160 plus confirmed kills, Kyle says: "I'm willing to meet my creator and answer for every shot that I took."
The most powerful moment in the trailer sees Kyle toying in the heat of the moment with whether or not to shoot an Iraqi child as he picks up a missile to aim at US troops.
Critics are tipping Cooper for his third consecutive Oscar nomination, after American Hustle and Silver Linings Playbook.
The US actor, 39, stars alongside Sienna Miller, Jack McDorman, Navid Negahban, Keir O'Donnell and Luke Grimes in the film adaptation of Kyle's memoir.
Kyle was killed at a shooting range at home in Texas in February last year by fellow veteran Eddie Ray Routh, who is currently awaiting trial for murder.
Cooper has described playing Kyle as "an honour". "There's something about how stoic [Kyle] was - it was all sort of in his eyes as a human being how gentle he was, how complicated he was," he told reporters at the film's New York premiere earlier this week.
American Sniper is set for UK release on 16 January 2015.Reuse content