Chewing gum does have a form of rubber in it. Gum contains gum base which is plastic and rubber. This is why gum does not dissolve in your mouth. Gum does not digest when it is swallowed. It stays in one piece and will stay in your body for a few days. Humans have used chewing gum for at least 5,000 years. Modern chewing gum was originally made of chicle, a natural latex. By the 1960s, chicle was replaced by butadiene-based synthetic rubber which is cheaper to manufacture. Most chewing gums are considered polymers.