In a blender, combine the first six ingredients; cover and process until blended. Pour into a large resealable plastic bag; add chicken. Seal bag and turn to coat; refrigerate for at least 1 hour.
Drain and discard marinade. Using long-handled tongs, moisten a paper towel with cooking oil and lightly coat the grill rack.
Grill chicken, covered, over medium heat or broil 4 in. from the heat for 4-7 minutes on each side or a meat thermometer reads 170°.
In a large salad bowl, combine the greens, red pepper, bean sprouts and peas. In a small bowl, whisk the dressing ingredients until smooth. Pour over salad and toss to coat. Cut chicken into strips; arrange over salad. Yield: 4 servings.