In a sauce pan over medium high heat, combine olive oil and butter. Add green onions and cook for 2 minutes. Add chicken broth and vinegar. Simmer for another 2 minutes until sauce begins to thicken. Stir in half of mint.
Preheat grill to medium. Sprinkle chops with salt and pepper and grill at medium heat until cooked to desired degree of doneness (160° for medium and 170°F for well done) as measured with meat thermometer. Add sear marks.
Place grilled lamb chops on platter, cover with sauce over top, garnish with remaining mint and serve.