Combine the cheese and bacon in a bowl.
Put the ground chuck in another bowl and sprinkle with salt and pepper; mix with a rubber spatula. Flatten a quarter of the meat mixture in the palm of your hand. Squeeze together about a tablespoon of the cheese and bacon mixture to make a little nugget; place in the center of the patty. Bring up the sides of the patty over the filling, making sure the cheese is completely covered; flatten slightly to shape. Repeat with the remaining meat and filling. Set the patties side-by-side on a platter and refrigerate while preparing the grill.
Place a large grill pan covering two burners over medium-high heat, or preheat an outdoor barbecue until very hot. Brush the grates with oil. Grill the burgers for 8 minutes per side for medium. Transfer to a clean plate.
Rub the grill grates with more oil. Grill the buns cut-side down for 1 minute to toast.
Serve the burgers with your favorite condiments and garnishes.