Rinse the chicken and pat dry with paper towels. Season the chicken with salt and pepper. Heat the oil in a saute pan over moderately high heat. Brown the chicken on both sides, about 8 minutes. Transfer the chicken to a plate and set aside. Reduce the heat to moderate. Add the onion and pepper, cover and cook, stirring occasionally, until the vegetables begin to soften, about 5 minutes. Add the mushrooms and cook, uncovered and stirring occasionally, until the mushrooms begin to brown. Add the garlic and cook, stirring, for 30 seconds. Add the wine and cook until reduced by half. Add the tomatoes and juice, oregano, red pepper flakes and 1/4 teaspoon of salt and simmer the mixture covered for 10 minutes.
Return the chicken breasts to the pan and simmer, covered, until the chicken is just done, about 20 minutes longer.