The possible parachute can be seen in The Plane Scene as CIA ends his interrogation of Ahyred Gunn, the second hooded man. While visibility is obstructed by CIA's jacket, proponents of the theory allege that the material is clearly an emergency parachute that CIA would use to survive the imminent crash. When Bane interrupts the interrogation of Ahyred Gunn, CIA may have been so shocked that he neglected to carefully hide the fact that he was wearing a parachute. However, it seems improbable that Bane noticed the parachute, as he later informed CIA that his master plan was to "[Crash] this plane with no survivors."
A slightly different version of the theory is that Bane knew of CIA's parachute, and an agreement between the two had been made prior to the plane scene in which Bane gave CIA the parachute. The "no survivors" comment that Bane made may have been in an effort to reassure Juan, who did not have a parachute, of his fate in the wreckage.