There are several ways to get gum off your car without harming the paint. It all starts with a bit of lubrication to help loosen the gum's grip on your car paint.
The best method is to use a product such as WD-40, which binds to the sticky oils on gum and makes it easy to wipe away with a damp cloth. Other products that can be used to lubricate the gum include peanut butter, body oil and baby oil. Be sure to use a non-toxic, organic product.
Next, use a plastic scraper (any metal may scratch the paint) to remove the bulk of the gum. It is important to work on a cool day so the gum will not melt. It is also recommended to park the car in a shaded area so that the sun will not heat up the surface of the paint while you are trying to scrape.
If the gum is still stuck, spray the spot with bug and tar remover. Let the solution soak into the gum spot for a few minutes to soften it. Scrape the loosened gum off your car with a plastic razor blade, working from the sides to the center of the spot. Be sure to keep the blade lubricated with bug and tar remover as you scrape. Reapply bug and tar remover to the spot as needed to continue softening the gum. Be sure to finish the process with a wash and dry of your vehicle.