In theory at least this can be bad, as excess acid secretion in combination with pockets of damage to the stomach lining may lead to an ulcer.
N fact as long as the gum is sugar
free (and particularly if it contains xylitol) it is actually good for the teeth and can prevent dental cavities.
However some moderation is necessary whichever type of gum he is eating. I'd suggest you limit him to thre.