How to Make It
Light a grill. Gently loosen the skin from the chicken breasts and stuff 4 oregano sprigs and a pinch of orange zest under the skin. Smooth the skin over the filling. Rub the chicken with oil and season with salt and pepper. Grill over low heat, skin side down, until browned and crisp, 12 minutes. Turn and grill until just cooked through, 15 minutes longer. Transfer the chicken to plates and let rest for 5 minutes.
Meanwhile, in a large skillet, melt the butter. Add the garlic and cook over low heat until golden, 2 minutes. Add the mushrooms and season with salt and pepper. Cover and cook over moderate heat, stirring a few times, until the mushrooms release their liquid, 4 minutes. Carefully pour off the liquid; you should have 1/2 cup. Continue to cook the mushrooms, uncovered, over moderately high heat, stirring often, until richly browned, 15 minutes. Add the parsley, lemon juice and the reserved mushroom liquid and season with salt and pepper.
Spoon the mushrooms over and around the chicken and serve.