Place the pillow in a freezer or place cold packs on top of the gum. Allow the pillow to freeze for two hours, then scrape off as much frozen gum as you can using a plastic knife or scraper.
Heat a cup of white vinegar until it comes to a boil. Dip an old toothbrush in the vinegar and rub it on the gum stain. Continue rubbing the gum, adding more vinegar when necessary, until the stain is gone.
Launder the pillow with regular laundry detergent to remove the vinegar smell. If the pillow isn’t machine washable, take it to the dry cleaners.