If shredding chicken it's best to do that while the chicken is warm, but allow any chicken to cool completely before mixing with mayo.
Mix the chicken with mayo first (this prevents the chicken salad from becoming watery as it sits if you are not eating it immediately)
Next, add in the celery, celery salt/seed, and add some additional salt if desired and black pepper to taste.
Alternatively, you can put all ingredients in the food processor and pulse it until the chicken and mayo have blended well and the chicken is in fine pieces, not in chunks.