Cook chicken breasts in steamer or bake in the oven until soft and tender. Let the meat cool and then cut into 1-inch pieces.
Combine dill, lemon juice, white pepper, garlic, salt, basil, and parsley with mayonnaise in a large bowl and mix everything thoroughly.
Add chicken, onion, celery, and carrots into the mayonnaise mixture and mix until well incorporated.
Cover the salad bowl and place it in the refrigerator for several hours (ideally overnight).
Serve the chicken salad on a bed of greens and enjoy!