Step 1

Season chicken with salt and pepper. In a deep 12-inch skillet, heat 2 tablespoons oil. Add chicken to skillet, skin side down. Cook over moderately high heat until browned, about 5 minutes. Turn chicken and brown other side, about 4 minutes. Transfer the chicken to a plate. Pour the oil out of the skillet and discard.

Step 2

Return skillet to moderate heat. Add remaining 2 tablespoons oil, shallots, garlic, and ginger; cook over moderate heat, stirring occasionally, until softened, about 2 minutes.

Step 3

Add sugar, vinegar, fish sauce, and 1/2 cup water to skillet. Bring to a boil, and return chicken to skillet, skin side down. Simmer over moderate heat, occasionally basting the chicken, 8 minutes. Turn chicken and continue basting, adding water by tablespoonfuls if sauce thickens too rapidly, until an instant-read thermometer inserted in thickest part of chicken registers 165° and sauce is thickened, about 15 minutes. Add jalapeño, and toss to coat in sauce. Transfer chicken to a platter, and drizzle sauce over the chicken.