Heat 1 tablespoon oil in large nonstick skillet over medium heat. Add chicken and sauté until cooked through, about 5 minutes per side. Cool. Cut chicken crosswise into 1/4-inch-thick strips.
Cook pasta in large pot of boiling salted water for 4 minutes. Drain well; transfer to large bowl. Add 1 tablespoon oil; toss to coat. Add chicken, snow peas, pine nuts and parsley; toss to incorporate all ingredients.
Whisk lemon juice and mustard in medium bowl. Add remaining oil in thin stream, whisking constantly. Season to taste with salt and pepper. Toss pasta with enough dressing to coat. (Can be made 3 hours ahead. Cover and refrigerate. Toss before serving.)