I was searching for ways to get peanut butter out of carpet and found these instructions claiming that peanut butter can actually be just the thing you need
to get gum out of your carpet. I was just as shocked as you, but reading through the reasoning it sounds like a great solution.
Scrape off as much gum as you can, then rub on some creamy peanut butter. The peanut butter will take the stick out of the gum. It should wipe away easily. Reading trough the instructions I thought "that's great, but what about my original problem of having peanut butter in the carpet?" Well, it turns out that isn't quite the problem I imagined it to be. A simple, homemade solution
will wash way the peanut butter and your carpet will be as stunning as it started (or in our house, will only have the stains that existed before the gum and peanut butter).