In a nonstick 12-inch skillet, bring 1 inch of water and salt to a boil over high heat. Add asparagus; return to a boil. Reduce heat to low; simmer, uncovered, 3 to 5 minutes, until asparagus is tender-crisp. Drain asparagus; set aside. Wipe out the skillet.
In a medium bowl, mix sugar, fish sauce, lime juice and soy sauce. Stir in chicken until evenly coated. (Coat chicken just before cooking, because the lime juice will change the meat's texture.).
Add 2 teaspoons oil to the skillet; place over medium-high heat. When oil is hot, add chicken; cook 5 minutes or just until it loses its pink color throughout, stirring occasionally. With tongs or a slotted spoon, transfer chicken to a clean bowl, leaving any cooking liquid in the skillet.
Add onion, ginger and jalapenos to the skillet; cook until onion is tender, about 8 minutes. Add onion mixture to the bowl with the cooked chicken.
In the same skillet, heat the remaining 1 teaspoon oil over medium heat until hot. Add asparagus; cook until it begins to brown, about 5 minutes, stirring occasionally. Return onion mixture and chicken to skillet; heat through.
Toss basil and cilantro leaves with chicken mixture just before serving.