In a small bowl, whisk together the vinaigrette ingredients. Cover and refrigerate.
To a nonstick skillet, add chicken, broth and vinegar. Boil; reduce heat- cover and simmer for 15 minutes or until juice of chicken is clear. Remove from heat. Uncover the skillet and let the chicken cool in the broth for 15 minutes. Refrigerate the chicken in the broth for 45 minutes (or until cool).
Remove the chicken from the broth; discard the broth. Cut the chicken diagonally into ¼-inch slices. Divide the chopped romaine among 4 serving plates. Arrange the chicken on top of the romaine. Top with berries. Drizzle vinaigrette over the salads.