Heat 2 tablespoons butter in heavy large skillet over medium heat. Add mushrooms, thyme and lemon juice. Season with salt and pepper. Sauté until mushrooms are golden brown, about 6 minutes. Add Marsala and boil 3 minutes. Add broth and reduce by 1/2, about 12 minutes. Remove and set aside.
Heat 2 tablespoons butter in heavy large skillet over medium heat. Dredge turkey in flour; tap off excess. Add turkey to skillet and cook until just cooked through, about 2 minutes per side. Transfer to plates and keep warm.
Place sauce back on heat. Bring to simmer and whisk in remaining 2 tablespoons butter. Season to taste with salt and pepper. Pour sauce over turkey. Sprinkle with chives and serve.
