Fill a pot with water, add a dash of salt, and bring it to a boil over high heat. While waiting for the water to boil, peel and quarter the potatoes. Once the water is boiling, add the potatoes and cook for 15-20 minutes or until tender.
Drain the water and return the potatoes to the same pot. Mash them with a fork, then mix in salt, pepper, butter, and milk until creamy. Set aside.
Season the chicken breasts with olive oil, salt, and pepper.