Preheat the grill to medium-high heat.
Pat the lamb chops dry with paper towels. Season both sides with 1 teaspoon kosher salt and 1/2 teaspoon black pepper.
Brush the lamb chops with 1 tablespoon olive oil on both sides.
Place the lamb chops on the grill and cook for 4 to 5 minutes per side for medium-rare, or until desired doneness is reached.
While the lamb chops are grilling, prepare the chimichurri sauce.
In a food processor or blender, combine the parsley, cilantro, red wine vinegar, garlic, red pepper flakes, 1/2 teaspoon kosher salt, 1/4 teaspoon black pepper, and 1 tablespoon olive oil.
Pulse until the herbs are finely chopped and the mixture is well combined but still slightly chunky.
Remove the lamb chops from the grill and let them rest for 5 minutes.
Serve the grilled lamb chops topped with a generous spoonful of chimichurri sauce.