Combine the first 9 ingredients in a medium bowl. Place the mushrooms in a stainless steamer set over simmering water. Cover and steam until just tender, about 5 minutes. Remove the steamer from the pot, set in the sink, and let the mushrooms drain a few minutes. Add the mushrooms to the bowl and toss to combine. When the mushrooms have cooled to room temperature, cover and marinate in the refrigerator at least two hours (can be made day before needed).
Preheat an indoor or outdoor grill to medium-high. Brush the chicken with 2 Tbsp. olive oil; season with salt and pepper. Grill 3 to 4 minutes per side, or until cooked through.
Toss the parsley into the mushrooms and serve alongside the chicken.