If you're not using rotisserie chicken, poach chicken breasts in simmering broth for about 20 minutes until fully cooked through. Let the chicken cool slightly, then shred it finely using a food processor or two forks. Fine shreds are key here; chunky pieces won't give you that classic Costco texture.
In a separate bowl, whisk together the mayonnaise, sour cream, lemon juice, garlic powder, salt, pepper, and celery salt until smooth. This dressing is really the heart of the whole recipe, so taste it before moving on and adjust the seasoning if needed.
Add the shredded chicken, diced celery, and diced onion into a large bowl. Pour the dressing over the top and gently fold everything together until every piece of chicken is coated evenly and nothing looks dry.
Cover the bowl and refrigerate the chicken salad for at least 30 minutes. This resting time lets the flavors meld together and firms up the texture, making it much easier to scoop or spread onto bread.
Once chilled, spoon a generous scoop of chicken salad onto your bread of choice. Add lettuce or extra crunch if you like, then top with the second slice and serve right away for the best texture.