Sweet Onion Chicken

6 tablespoons red wine vinegar (I've used other's ... just changes it a bit)
4 teaspoons sugar
1/2 teaspoons dried sage
1/2 teaspoons salt
4 skinless, boneless chicken breast halves (about 1 pound total)
2 teaspoons olive oil
2 large onions, halved and thinly sliced
1 cup reduced-sodium chicken broth, (I do homemade...)
1 tablespoon flour
1 carrot, cut into thing strips
1 red bell pepper, cut into thin strips
1/4 teaspoon freshly ground black pepper

1. In a shallow bowl, combine 3 tablespoons of the vinegar, 2 teaspoons of the sugar, 1/4 teaspoon of the sage, and 1/4 teaspoon of the salt and stir to blend. Add the chicken, toss to coat, and let stand while you prepare the onions.

2. In a large nonstick skillet, heat the oil until hot but not smoking over medium beat. Add the onions and the remaining 2 teaspoons sugar and cook, stirring occasionally, until the onions begin to brown, about 5 minutes. Stir in the flour, carrot, bell pepper, remaining 3 tablespoon's vinegar, remaining 1/4 teaspoon sage, remaining 1/4 teaspoon salt. and the black pepper and cook until the onions are very tender and caramelized, about 10 minutes longer.

3. Meanwhile, preheat the broiler or prepare the grill. Broil or grill the chicken 4 inches from the heat for about 4 minutes per side, or until the chicken is cooked through. Place the chicken on plates, spoon the onion mixture around the chicken and serve.

Suggested accompaniments: Garlic mashed potatoes. Fresh pear wedges sprinkled with cinnamon.