Butterfly chicken by slicing each piece across but not all the way through. Pound breast meat as thin as possible, 1/8- to 1/4-inch thick. Season chicken with salt and pepper.
Combine juice of 1 lime in a shallow dish with 1 teaspoon cumin, oregano, 2 cloves finely chopped garlic, and about 3 tablespoons of vegetable oil. Turn chicken to coat in marinade. Do not let chicken set longer than 10-15 minutes in marinade because of the acid content.
Heat griddle over 2 burners or a large skillet over medium-high heat. Grill chicken 3 minutes on each side to brown at edges.