Stir chicken and curry paste in medium bowl to coat. Set aside. Heat 2 tablespoons oil in heavy large skillet over medium-high heat. Add eggplant and green beans. Stir-fry until eggplant begins to soften, about 4 minutes. Add 1 tablespoon oil and chicken mixture to skillet. Stir-fry until chicken begins to brown, about 3 minutes. Add coconut milk; simmer until beans are tender, chicken is cooked through and sauce thickens slightly, about 3 minutes. Season with salt. Sprinkle with basil.