Chewing gum was a candy confection native to the planet Earth, which Humans often chewed. The concoction was often sweetened, with mint being a common flavor.
In 1969 Roberta Lincoln carried some spearmint chewing gum in her Peter Max designed handbag. (TOS novel: Assignment: Eternity)
During the 20th century, it was included with baseball player trading cards. Unfamiliar with this time period's custom of only chewing it and blowing bubbles, Beverly Crusher swallowed a replicated stick of chewing gum that was offered by a Dixon Hill holodeck police sergeant. (DS9 episode: "In the Cards", DS9 novel: Antimatter; TNG episodes: "The Most Toys", "The Big Goodbye")
In 2266, James T. Kirk used a wad of chewing gum to temporarily disable the controls of an elevator in Government House, allowing him to get close to Ilana. (TOS comic: "The Trial of Captain Kirk")
Miles O'Brien replicated his own recipe of chewing gum, with a Scotch whisky taste, and offered a stick to friend Julian Bashir. (DS9 episode: "Take Me Out to the Holosuite")