Mix preserves, vinegar, mustard and ginger in 2-cup glass measuring cup. Place ham in 6-quart slow cooker, trimming ham if necessary to fit. Brush ham with about 1/4 cup of the preserves mixture. Refrigerate remaining preserves mixture while ham cooks.
Cover and cook ham on Low heat setting 7 to 8 hours.
About 20 minutes before ham is done, microwave remaining preserves mixture uncovered on High 4 minutes. Stir in currants and lemon peel; microwave uncovered on High about 3 minutes or until mixture just begins to boil. Stir in chives. Cool about 10 minutes.
Remove ham from cooker. Slice ham; place on serving platter. Serve sauce with ham.