Steam green beans in a steamer basket on stove or in a microwave, until crisp-tender, about 5 minutes. Drain well; set aside.
Coat a large skillet with cooking spray and set over medium heat. Add jalapeno or chile and garlic; cook, stirring frequently, about 1 minute. Add 3/4 cup of coconut milk, curry paste, brown sugar, fish sauce and lemon grass; bring to a simmer.
Add chicken and reduce heat to medium-low; simmer, stirring occasionally, until chicken is cooked through, about 10 minutes. Add string beans and basil (mixture may separate). Add remaining 1/4 cup of coconut milk (sauce will be smooth again). Simmer until hot, about 1 minute more; remove garlic clove and serve over rice. Yields about 1 cup of chicken-string bean mixture and 1/2 cup of rice per serving.