Drain oysters; pat with paper towels to remove as much oil as possible. Coarsely chop. Halve hard cooked eggs lengthwise. Remove yolks and set whites aside.
Place egg yolks in a bowl; mash with a fork. Add mayonnaise, the 2 tablespoons snipped chives, mustard, pepper, and chopped oysters.
Mix well. Pipe or spoon egg yolk mixture into egg white halves. Garnish with snipped chives.