On a hot grill, grill chicken breasts until fully cooked. Season with salt and pepper. Refrigerate until cooled. Once cooled, julienne chicken breasts.
In a mixing bowl, combine chicken, red pepper, red onion, and apples.
In a separate bowl, combine mayonnaise and pesto. Combine the chicken and pesto mixtures. Season with salt and pepper. Serve on a bed of Bibb lettuce and endive.