Start your Grill on 'smoke' with the lid open until a fire is established in the burn pot (3-7 minutes). Preheat to 450F.
Place garlic, 1 1/2 teaspoons oil, butter and 1/8 teaspoon salt in food processor or blender and process, pulsing until the garlic is chopped finely.Transfer garlic butter to small bowl and stir in 2 teaspoons of the chives. In a small bowl, stir together 1 teaspoon salt, black pepper, and thyme. Rub both sides of each filet with the seasoning. Wrap each steak around its sides with a slice of bacon. Using the toothpicks, skewer bacon in place.
Grill steaks until lightly charred on the outside and until bacon is cooked, about 5 minutes per side for medium-rare. When done, remove steaks from fire and place on a warm serving plate. Remove toothpicks. Top each steak with the garlic butter and sprinkle with some of the remaining chives. Butter will start to melt and season the steaks. Serve immediately.
Note: Use tongs to flip steaks. Do not flip steaks with a fork or cut into the meat until ready to serve. Any cuts or punctures in the meat will cause juices to escape and dry out your steak.