Pulse shrimp gently in a food processor until just coarsely ground. Do not overblend. Combine ground shrimp and butter in food processor in a 2 to 1 ratio, and process until smooth (not too fine). Complete this step in batches if necessary until all shrimp and butter is used. Transfer to a large mixing bowl and add chives, lemon zest, and salt and pepper to taste. Mix well.