Chickens do eat ticks.
More Info: There has been a growing interest in raising backyard chickens for a variety of reasons including the healthy food source as well as for pest control. Chickens will eat ticks, fleas, mosquitoes, slugs, beetles, ants, maggots, grubs, caterpillars, grasshoppers, beetles, and even mice.
Why All the Interest in Raising Backyard Chickens? Utah State University Cooperative Extension
Natural Tick Predators
Besides the chicken, ticks do have other natural predators. Ticks are a favorite of the guinea fowl, which will also rid the yard of beetles and other such destructive pests. Most ground birds that feed on insects will eat ticks.
Fire ants are natural tick predators of the tick, though for obvious reasons wouldn't be a good choice to introduce to your landscape as a tick control measure.
How to Kill a Tick
You can kill a tick by dropping it in a vial with a small amount of rubbing alcohol, flushing it down the toilet, or freezing it. Hot air from the clothes dryer will also kill ticks hiding in your clothing.
Do not attempt to kill the tick while it is still attached to the body by suffocating with Vaseline or other such home measures. This will only cause the tick to regurgitate its contents into the host body, which increases the chance of disease transmission.