ChapStick in the carpet becomes an ever-expanding mess if not cleaned up right away. Remove the problem as soon as possible by picking up as much as you can with paper towels, then treating the remaining mess with rubbing alcohol and soapy water.
If the carpet has long fibers, separate them a bit with your fingers to locate all the ChapStick.
Pick up as much of the ChapStick as possible by grabbing it and lifting it straight up with a paper towel. Use a fresh part of the paper towel with each grab to avoid reapplying the material onto the carpet.
Scrape up any ChapStick that remains with the bowl of a spoon. Wipe the spoon bowl off with paper towels frequently. For a carpet with long fibers, grab the fibers in one hand to pull them straight up, then scrape the sides of the same fibers with the spoon your other hand.
Pour a little rubbing alcohol onto a lint-free white cloth. Dab the affected area of the carpet enough to wet the fibers with the alcohol. Move the carpet fibers around with your fingers a bit to work the alcohol in without spreading the ChapStick. Allow the alcohol to sit for a minute or so.
Rinse the spot with a small amount of warm water -- just enough to wet the fibers without soaking the carpet.
Blot the area with a dry lint-free white cloth. Continue blotting with a fresh area of the cloth until no more ChapStick comes up.
If any ChapStick remains, add a small squirt of a mild dish soap -- 1/4 teaspoon at most -- to a cup of water. Dip a lint-free white cloth into the water and dab the spot repeatedly. For a large stain, work from the outside edges toward the center to avoid spreading the lip balm.
Rinse the area by pouring a small amount of warm water over it, then blot it up with paper towels or a lint-free white cloth.
Rinse the area again with a little more warm water. Place a stack of folded paper towels atop the wet area, then add a heavy weight such as a stack of phone books to apply pressure. Replace the paper towels with fresh ones after 30 minutes or so if they are quite wet.