Meanwhile, season chicken with 1/2 teaspoon each salt and pepper. Heat 1 tablespoon butter in a large nonstick skillet over medium-high. Add chicken, and cook until golden and cooked through, about 4 minutes per side. Reserving drippings in skillet, transfer chicken to a plate and loosely cover with foil.
Return skillet to medium-high; add remaining 3 tablespoons butter and stir until melted. Add mushrooms and Brussels sprouts; cook, without stirring, until tender, about 5 minutes. Add stock, lemon juice, capers, and remaining 1/2 teaspoon each salt and pepper; bring to a simmer, and cook 1 minute.
Serve chicken sliced, over orzo and vegetables. Spoon sauce over the top and garnish with oregano.