Prepare grill or broiler.
Combine the first 8 ingredients in a small bowl. Brush the chicken with 2 tablespoons dressing; set remaining dressing aside.
Place chicken on grill rack or broiler pan coated with cooking spray; cook for 5 minutes on each side or until chicken is done. Cut into 1/4-inch-thick slices.
Combine the romaine lettuce and the next 4 ingredients (romaine lettuce through red onion slices) in a large bowl, and toss with the remaining salad dressing. Divide the salad evenly among 4 plates; top each serving with sliced chicken, and sprinkle with feta cheese.