Bring a large pot of salted water to a boil. Add shrimp and boil until pink and cooked through, about 2-3 minutes. Drain immediately and rinse with cold water to cool the shrimp. Chop into bite-size pieces.
In a medium bowl, toss shrimp with mayonnaise, celery, scallions, lemon juice and dill. Mix until thoroughly combined. Season to taste with salt and pepper.
Brush inside of potato rolls with melted butter. Distribute shrimp mixture evenly between rolls. Sprinkle rolls with Old Bay seasoning and top with crushed potato chips.