Bring a large pot of water to a boil over high heat. Add the chicken breasts and cook until fully cooked through, about 15 minutes. Remove with tongs, let cool slightly, then shred into bite-sized pieces using two forks or a meat shredder.
In a large mixing bowl, combine mayonnaise, lemon juice, minced garlic, dill, salt, and pepper. Whisk together until smooth and well incorporated, forming a creamy dressing.
Add the shredded cooked chicken to the bowl with the dressing. Stir thoroughly to coat all pieces evenly, ensuring each bit is moist and flavorful. Observe the mixture becoming uniformly coated and creamy.
Taste the mixture and adjust seasoning with additional salt and pepper if desired. Transfer the chicken salad to a serving dish or airtight container.
Cover and refrigerate the chicken salad for at least 30 minutes to allow flavors to meld. The final dish should be chilled, with a creamy texture and visible chunks of shredded chicken, ready for serving.
Serve the chicken salad chilled, garnished with additional herbs or sliced vegetables if desired. It can be enjoyed on sandwiches, with crackers, or as a standalone salad.