In principle, you are not allowed to have any food or calorie intake during the fasting hours.
However, because many other types are very low in calories, chewing a stick or two of sugar-free gum each day is unlikely to significantly affect your fast. So you’d better check the label to confirm if it has many calories or not.
And chewing gum has many benefits as well. What could be very beneficial during fasting is that it can decrease hunger and appetite.
A 2015 study showed that chewing gum over 30 minutes could increase satiety and stabilize levels of Glucagon-like peptide 1, a hormone that can decrease appetite.
Therefore, chewing gum can help you overcome hunger and make it easier to keep with your fasting plan.