Firstly, get some goof-off. This is a heavy-duty stain and spot remover. Where to get it, you must be wondering? It is available at most hardware/grocery/drug/department stores and even online. “Goo Gone” is the name of the product which works very well in such situations.
Spray a little Goof Off on the affected area with gum (make sure it doesn’t remove colour).
Then scrape it off with a butter knife.
Get a paper towel to remove the remaining residue of the chewing gum.
Put the garment outside so that Goof Off evaporates completely.