1. Place beef in large mixing bowl. Use spatula to fold in horseradish and chives; season with salt and pepper.
2. Hand form the meat into 8 burgers, cover them, and chill in fridge while preparing grill.
3. Place a large grill pan on 2 burners over medium-high heat or preheat gas or charcoal grill and get it very hot. Wipe hot grates with some oil for non-stick grilling surface.
4. Grill burgers for 8 minutes per side for medium; 7 minutes per side for rare.
5. When burgers are just about cooked, put a couple of slices of cheese on top and cover for about 1 minute.
6. Toast buns, cut-side down for 1 minute. Serve burgers with condiments and garnish as you like.
