In a bowl, combine the coconut milk, chicken broth, fish sauce, lime juice, soy sauce, brown sugar and cornstarch.
Slice the chicken breast into long strips. Heat 2 Tbsp. of oil in a skillet over medium heat. Cook chicken until browned on both sides and juices run clear, about 8 minutes per side. Remove from the skillet and set aside.
Add the remaining tablespoon of oil, green beans, peppers and garlic to the pan and saute until slightly softened, about 3-4 minutes. Reduce heat to low and add chicken back in. Stir in the coconut milk mixture and simmer until thickened. Remove from heat and stir in the Thai basil and jalapeños.
To make the rice, bring coconut milk, chicken broth, sugar and salt to a boil. Stir in the rice and lower heat. Cover and simmer, stirring occasionally, until most of the liquid is absorbed. Fluff with a fork.