Cook the noodles according to the package directions. Drain and rinse under cold water.
Meanwhile, heat the olive oil in a large skillet over medium heat.
Season the chicken with ½ teaspoon salt and ¼ teaspoon pepper and cook until browned and cooked through, 4 to 6 minutes per side.
In a small bowl, combine the lime juice, sesame oil, sugar, and jalapeño.
Slice the chicken. Divide the noodles, chicken, watercress, cucumber, and scallions among plates. Drizzle with the dressing.