Many mushrooms are too delicate for the grill. Button mushrooms stand up well, as do shiitake, cremini, and portobello. When grilled, the smoky flavor is incredible. In this dish, they are tucked beneath the chicken skin for extra flavor.
In a large skillet heat olive oil over medium heat. Add mushrooms, garlic, and oregano. Cook until mushrooms are lightly browned and tender, 6 to 8 minutes, stirring occasionally. Remove from heat. Stir in Marsala, anchovy paste, 1/4 teaspoon salt, and 1/4 teaspoon pepper. Return to heat and cook and stir 2 minutes more. Remove from heat and allow to cool slightly, about 10 minutes.
With your hands, loosen skin of each chicken piece on one side. Stuff mushroom mixture evenly beneath the skin. Sprinkle chicken lightly with salt and pepper
For a charcoal grill, arrange medium-hot coals around a drip pan. Test for medium heat above the pan. Place chicken pieces, bone sides down, on grill rack over drip pan. Cover and grill for 50 to 60 minutes or until chicken is no longer pink (170 degreesF for breast halves, 180 degreesF for thighs and drumsticks). (For a gas grill, preheat grill. Reduce heat to medium. Adjust for indirect cooking. Place chicken pieces on grill rack; grill as above.)
Serve with fresh lemon and garnish with oregano. Makes 4 to 6 servings.