Grill or bake the chicken until it is cooked through and no longer pink in the center. If baking, place in a sprayed and oiled baking sheet. Place the chicken in the pan, season with salt and pepper and put a layer of tinfoil on top of the pan. Bake the chicken at 350 for 25-30 minutes, or until the center of the chicken is cooked through. When the chicken is finished baking or being grilled, remove it from the stove or grill and let it rest for a few minutes to cool down. Once the chicken is cooled, cut the chicken into small pieces and get rid of any of the excess fat. Place the chicken pieces in a large bowl. Dice the red onion and celery fine and place in the bowl as well. Add the remaining ingredients to the chicken and toss until coated. If the salad needs a little more moisture, add extra mayonnaise and lemon juice. Season to your liking and then serve on a bun or in large pieces of lettuce.