Combine the lime juice, oil and all seasonings. Pour over the chicken cutlets, move the chicken around to make sure each piece is well coated. Cover and refrigerate for 30 minutes to 1 hour.
Heat grill to medium high. Cook chicken on both sides until the juices run clear and the center is no longer pink. Do not over cook. Cooking time will vary according to grill temperature and thickness of cutlets.
For the Pico
In a medium sized bowl, combine all ingredients well. Let sit at room temperature for at least 30 minutes before serving, stirring occasionally.