Setting out traps and spraying a solution of cayenne pepper and water are two effective ways to exterminate chipmunks. These methods work for chipmunk burrows in the yard and for the ones that find their way into the attic or other crevices in the home.
Sprinkling cayenne, or another spicy pepper, into a spray bottle with water makes a remedy that sends chipmunks away, but they like to come back to their burrows, so it is necessary to apply the spray repeatedly. It is also difficult to find burrow openings, so knowing just where to spray the repellent is tough when dealing with these pests in the yard.
Trapping takes some more work, but is generally more effective against a community of chipmunks. Some forms of bait that chipmunks enjoy include peanut butter, cereal or nuts. Placing traps near areas where chipmunks have shown up before leads to a higher rate of success. Either conventional or glue traps work to catch chipmunks.
People who are willing to take the time to put the traps in the car and relocate the chipmunks several miles away might prefer no-kill traps. It is important, though, to release the chipmunks somewhere where they do not pose a nuisance to anyone.