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)
Background information Edit
With Christine Chapel having become a very popular character, fans were extremely excited about possibly seeing her in the alternate reality introduced in the movie Star Trek. Recalled co-writer Roberto Orci, "Even before the first movie came out, a lot of online chatter was, 'Is Nurse Chapel gonna be there?!'" 
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)
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. 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 actually be Nurse Chapel.
In the lead-up to the release of Star Trek Into Darkness, some fans guessed that Alice Eve might be portraying Nurse Chapel.  This was later disproved, though, with Eve instead playing Carol Marcus. The screenwriters opted to nevertheless reference Chapel in the film. "We just figured that would be a great reference," noted Alex Kurtzman. The way it helped establish Kirk's attitudes to women, such as that he forgot Chapel, was the reason the in-joke was used. 
When asked if Chapel could actually appear on the Enterprise after being referred to Star Trek Into Darkness, Roberto Orci laughed and stated, "That's certainly possible!"