Step 1In a large, deep saucepan, combine the brown sugar, granulated sugar, soy sauce and water and boil over medium-high heat until reduced by about 1/3, about 30 minutes. Set aside to cool. This makes 1½ cups of sweet soy sauce.
Step 2Boil the noodles until tender, then place in a bowl of ice water to cool. Drain and reserve.
Step 3Mix together 2 tablespoons of the cooled sweet soy sauce with the black vinegar and the garlic and reserve.
Step 4To serve, place the bean sprouts in the middle of a medium bowl. Mound the noodles in the center of the bowl over the bean sprouts. Spoon the sauce mixture and then the chile oil over the noodles. Top with the chicken and green onion and serve.