Drain oysters, reserving 1/2 cup oyster liquor. Coarsely chop oysters; set aside. Combine flour and lemon rind in a small bowl.
Combine reserved oyster liquor, milk, and butter in a large saucepan over medium heat, stirring until butter melts. Add flour mixture all at once, beating vigorously with a wooden spoon 1 minute or until mixture leaves sides of pan. Remove from heat. Add eggs, 1 at a time, beating vigorously with a wooden spoon after each addition until smooth. Fold in oysters and chives.
Pour oil to depth of 2 inches into a Dutch oven; heat to 375°. Drop oyster mixture by heaping tablespoonfuls into oil. Fry, in batches, 2 to 3 minutes or until golden. Drain on wire racks. Serve immediately with Caper Dipping Sauce.