Chapel was on staff in the medical bay when James T. Kirk, whom McCoy had smuggled aboard, began to experience a severe reaction to a Melvaran mud flea vaccine he had been injected with. As Kirk's hands began to swell, McCoy called for Chapel to prepare the necessary medication to cure the affliction. (Star Trek)
Chapel and Kirk had a relationship at some point. Following Kirk's promotion to captain of the Enterprise, Chapel left to become a nurse on the outer frontier. Carol Marcus, who was a personal friend of Chapel, brought up Chapel in a conversation with Kirk, but he did not seem to remember her. (Star Trek Into Darkness)
Although not seen directly on screen in the film, Chapel's presence on the Enterprise is established in dialogue. McCoy calls for "Nurse Chapel" just after Kirk's hands swell up from the vaccine.
In an interview with screenwriters Alex Kurtzman and Roberto Orci, Kurtzman explained, "In our original, original draft we wrote some scenes with Nurse Chapel but ended up losing them. Even in our first draft it's not included. We originally had a flirtation between her and Spock: Nurse Chapel was obviously really obsessed with him and he was not giving her the time of day, which we thought was funny, but then we came onto the Spock/Uhura connection [established in the film] and that's why Nurse Chapel ended up by the wayside." (Star Trek Magazine, issue 146, p. 38)
Near the end of the film, as Kirk, Spock, and Pike beam back from the Narada, a blond-haired female medic with a 1960s-style beehive hairdo is seen administering to Pike. This could be Nurse Chapel.