Rabbi Yehuda Bukspan of Los Angeles has ruled that all standard gums are kosher.
Marc B. Shapiro writes: “I wonder if R. Moshe would agree with R. Yitzhak Abadi that all the standard gums (Wrigleys, Trident, etc.) are kosher.”
The kashrut organizations assume that gum needs a hashgachah. Here is what R. Zushe Blech has to say on the subject
The need for reliable Hashgacha for gum stems from many ingredient concerns. Plasticizers can be pure lard or tallow and emulsifiers are also often made from animal fats. Flavors and glycerin can also be completely non-Kosher. Even if all of the ingredients in a Kosher gum were acceptable, the equipment on which the product is made requires a Kashering from non-Kosher productions. Although the gum itself is not swallowed, these fats and flavors migrate from the gum into the mouth.
See here. (What does Blech mean by “reliable Hasghacha”? Does it mean that hashgachot that disagree with his understanding are not “reliable”?)
Let’s leave flavors out, as none of the flavors in the major gums are non-kosher. Let’s also leave out the issue of equipment, since this is not a real halakhic concern (as anyone who has ever lived in a place other than Israel and America, and thus has to buy foods without hashgachah, is well aware.) The issue is glycerin, emulsifiers etc. I don’t understand why this should be a problem. Even assuming that it is forbidden to swallow these things as part of a food, why would it be prohibited to simply chew on these tasteless items? Is there any kashrut problem when my son chews on his pigskin baseball glove while waiting patiently for a ball to be hit to him?