Ken Kesey, the novelist who wrote the book One Flew Over the Cuckoo's Nest seized on Juicy Fruit for its symbolic value. The novel uses a huge Native American as the protagonist who tells the story of "Mac" who arrives at 60's style insane asylum as a messianic figure ... of sorts. Mac is full of life, vim and vigor; his mental illness appears limited to a lack of tact and a disrespect for rules. To the other, truly injured patients, Mac carries a message of freedom and hope. In this scene, "the Chief" as he is called, opens up to Mac in an exchange over a stick of Juicy Fruit gum.
In the scene above, we learn that the Chief is not deaf and dumb, but just hiding in the asylum as a defense against his fears of an outside world that has treated him, and his people, with cruelty and disregard. In the scene below, you'll see the Chief in an earlier sequence, still in disguise, looking on as Mac tries to lead the group in an escape toward the pleasures of the outside world.
In the final scene of the movie -- perhaps the best movie ending I've ever seen -- the Chief is horrified to find that Mac has been given a frontal lobotomy, effectively killing off the essential aspects of his personality. Watch as the Chief decides to carry Mac with him in a long-awaited quest for freedom, just as we carry the Holy Spirit inside of us in our own life journeys.