Heat oil in a skillet over medium heat. Add curry paste and cook until fragrant. Stir in half the coconut milk until smooth. Add chicken and cook until partially cooked. Pour in remaining coconut milk, fish sauce, sugar, and kaffir lime leaves. Simmer 10 minutes until the chicken is cooked and the sauce thickens. Add bell peppers and cook a few minutes. Garnish with Thai basil and serve with jasmine rice.
Notes
Adjust curry paste amount to control spice level. Full-fat coconut milk creates the creamiest texture.