Gum that contains the ingredient Xylitol which is an artificial sweetener is extremely toxic to dogs and even one piece of gum might prove fatal for a dog if ingested.
But most times the dog will have to eat 2 or 3 pieces of gum with the Xylitol before it gets to the point to where it kills the dog.
You should keep the gum out of reach of the dog and if the dog does ingest one piece of gum you should keep an eye on the dog and if you notice any sudden changes in the dogs health then take the dog to the vet.
I had a dog that ate one piece of gum that contained Xylitol and he was actually fine although I did call the vet and the vet said to just keep an eye on him and if his health changed then bring him to the vet.
If the dog ate more than one piece of gum then the vet said I should bring him to the vet to be checked out but one piece while possible is unlikely to hurt the dog.