Cook the rice according to the package directions.
Meanwhile, season the chicken with ½ teaspoon salt and ¼ teaspoon pepper. Heat the oil in a skillet over medium-high heat.
Cook the chicken in batches until golden brown and cooked through, about 2 minutes per side. Remove from skillet and cut into strips.
Add the bell peppers and ¼ cup water to the skillet and cook, stirring frequently, until just tender, 3 to 4 minutes.
Add the coconut milk and curry paste and simmer for 4 minutes. Stir in the chicken.
Spoon the chicken curry over the rice and sprinkle with the basil. Serve with the lime.