Ina large pot of boiling water, cook the orzo until just tender. Drain well.
Meanwhile, on a sheet of waxed paper, combine the flour, salt and pepper. Dredge the chicken in the flour mixture, shaking off and reserving the excess. Thinly slice the lemon half and set the slices aside. In a jar with a tight-fitting lid, combine the lemon juice, wine, broth, and reserved flour mixture and shake until smooth.
In a large skillet, heat the oil until hot but not smoking over medium heat. Add the chicken and cook until lightly browned, about 2 mintues per side. Add the garlic and mushrooms and cook, stirring frequently, until the mushrooms are slightly softened, about 2 minutes.
Shake the lemon juice mixture and add it to the pan, stirring to combine. Bring to a boil, reduce to a simmer, and cook until the chicken is cooked through, about 5 minutes. Add the lemon slices and cook for 1 minute. Divide the orzo among 4 plates and spoon the chicken mixture on top. Sprinkle with the capers and parsley (if using) and serve.