Combine first 6 ingredients and salt and pepper to taste in a bowl. Whisk until smooth. Cover and chill . Prepare grill or broiler. Season chicken with salt and pepper to taste. Grill or broil 4-5 minutes per side, until just cooked throughout. Cut diagonally across the grain into 1/4 inch slices. Divide lettuce between individual serving plates. Pour dressing over. Top with sliced chicken breasts.
