Assuming your dog didn’t also eat the packaging of the gum, immediately read the label on the packaging. Many gums contain xylitol, a sweetener which is toxic for dogs. If you see this ingredient in the gum, your dog needs prompt emergency veterinary intervention. If the gum does not contain xylitol, you should still call, contact, or visit your veterinarian and follow their instructions. They may advise you to monitor your dog for a while, to bring your dog in, or to keep an eye out for certain signs.