Rub whole heads of garlic with oil. Season with 1/8 teaspoon salt. Place in microwave-safe pie plate. Cover with microwave-safe plastic wrap. Microwave at full power (100 percent) for 5 minutes. Let stand 5 minutes. Garlic should be softened.
Slice heads of garlic in half horizontally. Squeeze skins, pushing out roasted pulp into bowl. Mix mayonnaise, lemon juice, 1/2 teaspoon salt, pepper into garlic.
Rub the chicken breasts with 1 tablespoon olive oil. Heat remaining tablespoon oil in skillet. Add chicken; sauté 2 to 3 minutes on each side or until browned. Serve with garlic mayonnaise. Garnish with basil or parsley if you wish.