To remove chewing gum from carpet, get out your electric hair dryer and some Ben Gay.
Step by Step
Step 1: Heat the gum, being careful not to melt the carpet fibers. Its a good idea to test in an inconspicuous area first, such as the inside corner of a closet.
Step 2: Use a piece of plastic wrap or a plastic bag to lift the softened gum away. Just allow it to stick to the plastic, then pull it up. This may get most of it.
Step 3: Next, apply Extra Strength Ben Gay, or another muscle rub containing methyl salicylate. Again, test this in an inconspicuous area first.
Step 4: Use plastic again, or a rag to pull more gum out. Repeat if necessary. Once you completely remove the chewing gum from the carpet, clean the area with a mild detergent solution (a few drops of dish soap in a cup of warm water will work). Rinse with warm water and dry the area.
Using Commercial Carpet Stain Removers
Some common carpet stain removers will work to remove chewing gum from carpet. Goo Gone, in particular, works fairly well. Pull out as much gum as you can, then heat what remains. Apply Goo Gone, using a brush or the edge of the cap to work it in and break up the gum. Pick it out a piece at a time. Patience is required. Repeat the process until you remove all the gum.
Be sure to thoroughly rinse the spot. Use a shop-vac if you can, or just rinse and blot with a white cotton cloth repeatedly. It is important not to leave any cleaning solvent in your carpet for too long, and to rinse it completely.
If you cannot remove the chewing gum from the carpet using either of the two methods here, don’t worry. A carpet cleaner with a hot water extraction unit (a steam cleaner) can get usually get it out.