Antonyms for the phrase "chums together" could include words such as distance, separate, isolate, exclude, or segregate. These terms suggest ideas of being apart or removed from others, instead of being in close proximity and forming bonds of friendship. While "chums together" implies a sense of unity and camaraderie, these antonyms suggest a lack of connection or division between individuals. Perhaps in certain situations, there may be a need to maintain distance or focus on individuality, but in many cases, the opposite of chums together can lead to feelings of loneliness and isolation.