1) Place flour in a shallow bowl. Cut each chicken breast in half on the diagonal to make about 4 roughly equal portions; sprinkle with 1/8 teaspoon salt and pepper. Dredge the chicken in the flour and transfer to a plate. Reserve 2 tablespoons of the flour.
2) Heat 1 tablespoon oil in a large skillet over medium heat. Add the chicken and cook untill brown on both sides, about 2 minutes per side. Transfer to a plate.
3) Add the remaining tablespoon oil to the pan. Add mushrooms, onion, rosemary, and the remaining 1/8 teaspoon salt, and cook, stirring frequently, until the onion is soft and golden brown, about 5 minutes. Sprinkle the vegtables with the resvered flour and cokk, stirring, until coated. Add wine to the pan and cook, stirring for 1 minute. Add draind tomatoes, broth, roasted red peppers, and olives; bring to a lively simmer over medium to low heat.
4) Return the chicken to the pan and continue cooking, stirring once or twice until the liqud has thickened slightly and the chicken is cooked all the trough, about 10 minutes. Serve the chicken with the sauce granished in rosemary, if desired.
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