Put the rice into a medium pot and pour in 6 cups cold water. Put the pot over medium-high heat, cover, and bring to a boil. Reduce the heat to a simmer and cook until the water is absorbed, 20 to 30 minutes. (Reserve 2 cups cooked rice for Rice Pudding with Coconut Milk recipe.)
Remove the chicken breasts from the bone and slice into thin strips. (Reserve the bones and the legs, thighs, and wings for Round 2 Recipe Coconut Chicken Soup.) In a large wok or skillet over high heat, add the oil. When the oil is hot, add the chicken and stir-fry until it is almost completely cooked through, 3 to 4 minutes. Add the onions and peppers and cook until slightly softened but still crisp, about 3 minutes. Add the chile and garlic and cook 1 minute.
To a bowl, add 2 tablespoons water, sugar, soy sauce, and fish sauce. Stir and pour over the chicken and onions and cook for another minute. Add the basil and remove from the heat once it has wilted. Add the lime juice into the chicken mixture and stir. Serve hot over rice.