Combine first 5 ingredients in processor. Process until smooth. Place chicken pieces in 15x10x2-inch glass baking dish. Sprinkle chicken with salt and pepper. Pour tarragon-mustard mixture over chicken; toss to coat. Let stand at room temperature 1 hour or refrigerate 2 to 4 hours, turning occasionally. Prepare barbecue (medium heat). Place chicken on barbecue. Cover and grill until chicken is almost cooked through, turning every 5 minutes and basting with marinade, about 30 minutes. Grill without basting until chicken is cooked through, about 7 minutes longer. Serve chicken hot, warm, or at room temperature.