In a large glass bowl combine the oil, vinegar, lime juice, and dry salad dressing mix. Mix together. Add chicken strips, onion and bell pepper. Cover dish and refrigerate. Marinate for 3 to 6 hours.
In a large skillet, heat oil. Remove chicken, onion and bell pepper from marinade and saute in oil until chicken is cooked through (juices run clear) and onion is translucent.
