Cut away the peel and pith of the grapefruit; cut into segments.
Season the chicken cutlets and cook in olive oil, in batches, until cooked through, 3 minutes per side; remove. Add grapefruit juice and chicken broth to the pan. Simmer for 6 minutes. Stir in 3 tablespoons butter. Top the chicken with the sauce, segments, toasted walnuts, and chopped parsley.