To make the dressing, stir together the vinegar, chives, salt, pepper, lemon zest, and lemon juice in a small bowl. Whisk in the oil until well blended and set aside.
Combine the apple, celery, cabbage, radish, and pepper in a large serving bowl and toss with the dressing (which you should feel free to elaborate on with your own spice concoction; personally, I love adding sesame oil and crushed peanuts to slaws).
Refrigerate for a few hours before serving to let the slaw soak up all the flavors. It’s even better the next day! Serve chilled.