If vinegar doesn't work, there are numerous chemical gum removers that can be found at your local hardware store.
Chewing gum can become a sticky, difficult mess when not cleaned up immediately. When you're dealing with an old, hard piece of chewing gum stuck to a surface, dissolving is often the best method of removal if scraping and applying oil aren't working. Luckily, you can dissolve the bond between chewing gum and the surface it's sticking to with ordinary household vinegar.
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Loosen the gum as much as possible from the surface it's on. Use a paint scraper, or dull knife to separate it as much as possible from the surface.
Pour 1/2 cup of vinegar into a microwave safe bowl. Place it in the microwave, and heat it until the vinegar is warm.
Pour the vinegar over the piece of gum. Saturate the area completely.
Allow the vinegar to sit for 5 to 10 minutes.
Tug on the gum to loosen and remove it from the surface.