1. Season fish with salt and pepper. Put in a 1-gal. resealable plastic bag and add marinade. Seal bag and marinate at room temperature about 20 minutes. Drain, saving garlic, and discard marinade. Blot fish and garlic with paper towels to avoid dripping alcohol near the heat.
2. Heat oil in a large nonstick frying pan over medium-high heat. Add fish, garlic, and olives. Cook fish until browned on one side, 3 to 4 minutes. Turn over and cook until cooked through but still moist in the center, 2 to 3 minutes more. Remove pan from heat and transfer fish to a platter, leaving garlic and olives in pan.
3. Pour lemon juice and chicken broth into pan and stir to pick up brown bits, then stir in vermouth and gin. Return pan to high heat and boil until reduced by half, about 3 minutes. Stir in butter to thicken. Pour sauce with olives and garlic over fish.
Note: Nutritional analysis is per serving.