Mix brown sugar, water, fish sauce, green onion, jalapeno pepper, soy sauce, and garlic together in a bowl.
Heat olive oil in a skillet over high heat. Add chicken and brown on all sides, about 3 minutes per side.
Pour 1/3 brown sugar mixture into the skillet. Cook on high heat until thickened and caramelized but not blackened, about 5 minutes. Add remaining mixture; simmer until chicken is no longer pink in the center and the juices run clear, about 5 to 7 minutes more. Remove from heat, cover, and let sit to thicken further, about 5 minutes.