Heat oil over medium-low heat in a large nonstick pan. Add the light scallion parts, garlic, and jalapeño. Cook, stirring, for 3 to 4 minutes until softened but not browned.

Whisk in coconut milk, red curry paste, fish sauce, and brown sugar. Bring to a gentle boil, then reduce heat and simmer for a few minutes until slightly thickened.

Add chicken pieces and simmer uncovered, stirring occasionally, for 5 to 6 minutes until the chicken is cooked through. Keep heat moderate for tender results.

Stir in lime juice, dark scallion greens, and cilantro. Adjust seasoning as needed and serve over steamed jasmine rice.