Preheat an outdoor grill or a grill pan to medium-high heat. Combine the chicken, salt, pepper, mustard, bread crumbs, lemon juice, and chives in a large bowl. Form into four ½-inch-thick patties.Grill the patties, flipping once, until the juices run clear (the center should register 160°F on an instant-read thermometer), 8 to 10 minutes. Top the patties with the cheese during the last minute of cooking, if using, and cover the grill or pan to melt it.Meanwhile, lightly grill the cut side of the buns, if desired. Serve with any or all of the following optional garnishes: Sliced tomato, sliced red onion, lettuce, mayo, Dijon mustard, and pickles.