Place flour in a flat bottomed dish with high sides, like a pie plate. Season both sides of the chicken cutlets with salt and pepper and dredge through flour, shaking off any excess.
Melt butter and olive oil in a large skillet over medium-high heat. Add chicken to the skillet and cook golden; about 4-5 minutes per side. Remove from heat and transfer chicken pieces to a paper towel lined plate.
Make the sauce. Melt 3 tablespoons butter in the skillet, scraping up the brown bits on the bottom. Whisk in flour until smooth and cook until golden; 1-2 minutes. Gradually stir in chicken broth and simmer until thickened. Stir in lemon juice and capers.
Taste and add a pinch or two of salt and pepper, then return the chicken to the pan. Simmer for 5 minutes., then stir in fresh parsley. Serve immediately.
Serve over this pasta, like angel hair, or mashed potatoes.
If you can't find chicken cutlets, use regular chicken breasts pounded this, or cut to size.