Preheat the broiler. In a cup, combine 1/2 tsp of oregano, 1/4 tsp of cumin, the rosemary, and salt. Rub chicken with the mixture.
Place the chicken and the bell pepper halves. Broil the chicken 4-inches from the heat for about 4 minutes per side or until cook through. Transfer the chicken to a cutting board. Continue to broil the pepper halves for 4 minutes longer or until skin is blackened. Transfer the pepper to a small bowl, cover with plastic wrap and let stand for 5 minutes.
Meanwhile, cut the chicken into bit size pieces. Transfer the peppers to cutting board. Peel off the blackened skin from peppers, remove any seeds and cut into strips.
In a bowl, combine the vinegar, ketchup, oil, cayenne, remaining oregano, and cumin. Add peppers, water chestnuts, orange sections, and green leaves(any type) and toss. Put onto 4 plates and place chicken on top, sprinkle with pecans and enjoy.