Place the chicken in the bottom of a cold slow cooker. Season with salt and pepper, then add about one-third of the BBQ sauce and stir to coat the chicken.
Cover and cook on high for 3–4 hours, or until the chicken is fully cooked and tender.
Remove the chicken to a large shallow dish and shred it with two forks.
Return shredded chicken to the dish and stir in another one-third of the BBQ sauce and any cooking liquid until the chicken reaches your desired saucy consistency.
Preheat the broiler. Place the slider roll bottoms on a baking sheet. Divide the shredded BBQ chicken so each bottom gets about 1/4 cup, then sprinkle each with about 1 tablespoon grated cheddar.
Broil the assembled bottoms 30 seconds to 1 minute, or until the cheese is completely melted. Top with dill pickle chips if using, then add the roll tops and serve immediately.
