Place the fabric in a refrigerator, if possible. Leave it there for approximately two hours to harden the wax elements of the ChapStick.
Remove the fabric and then scrape or snap off as much now-brittle ChapStick as you can with a blunt knife.
Place a clean white cloth on either side of the stain and press the cloths with a warm iron. Change the cloths as they become stained with ChapStick. Continue pressing and changing cloths until no more stain is being removed.
Boil a kettleful of water. Pour this boiling water through the stain over a sink.
Wet a clean cloth with dry-cleaning solvent, available from grocery stores. Dampen the stain with this cloth.
Mix together a solution of one part chlorine bleach, using color-fast bleach if the fabric is not white, to three parts clean water in a container. In addition, mix together a solution of one part white vinegar to two parts clean water.
Apply the bleach solution over the stain with an eye-dropper, available from grocery or drug stores, to wet it. Leave this solution on the fabric for 30 seconds.
Rinse away the bleach solution under the faucet. Rinse further with the vinegar solution to remove any remaining bleach.
Wash the fabric in as hot a temperature as the manufacturer recommends. Hang it outside and allow it to dry.