1. Preheat broiler. Place greens and red onion in a large bowl. In a small bowl, whisk together olive oil, vinegar, mustard, garlic, tarragon, salt, and pepper. Pour about three-quarters of dressing over greens and toss to coat. Divide among 4 plates. Arrange chicken on top.
2. Broil bread about 4 inches from heat about 1 minute, until one side is lightly toasted. Turn bread over and place cheese on top. Broil until the cheese melts, about 1 minute longer.
3. Set Brie toasts at side of each salad and serve at once.