Cut chicken into bite-sized pieces. Chop onions and peppers into rough 1-inch pieces. Mince garlic and crush kaffir lime leaves to release their oils.

Heat a large skillet over medium-high heat. Add coconut oil, then onions and sauté for 1 minute. Add peppers and garlic, cooking 2 to 3 minutes more.

Push vegetables to the sides of the pan. Add curry paste and peanut butter to the center and sauté for 2 to 3 minutes to intensify the flavor.

Add kaffir lime leaves, coconut milk, and fish sauce. Stir everything together until well combined.

Add chicken and bring to a boil. Lower heat and simmer for 10 to 15 minutes until chicken is cooked through and sauce has thickened. Stir in basil leaves and serve over rice.