Cook carrots and peas in boiling water for 2 1/2 minutes or until crisp-tender. Drain and rinse with cold water; drain.
Combine the carrot mixture, lettuce, watercress, radishes and parsley in a large bowl. Set aside.
Place the chicken between 2 sheets of plastic wrap; pound to 1/4 inch thickness unsing a meat mallet or small heavy skillet. Sprinkle chicken with 1/4 teaspoon salt and 1/8 teaspoon pepper.
Heat 2 teaspoons oil in a large skillet, swirling to coat. Add the chicken to the pan; cook 4 minutes on each side or until done. Let stand 5 minutes; cut across the grain into slices.
Combine the remaining 2 tablespoons oil, remaining 1/4 teaspoon salt, remaining 1/8 teaspoon pepper, vinegar, and remaining ingredients in a small bowl, stirring with a whisk. Drizzle the dressing over the lettuce mixture; toss gently.
Arrange about 2 cups of lettuce mixture on each of 4 plates; divide the chicken evenly among the servings.