For the roasted shallot vinaigrette:
1. Preheat oven to 350°F.
2. With the skin on, cut the shallot in half lengthwise. Spray a baking sheet with non-stick spray. Drizzle the shallot with a bit of the olive oil and place them on the baking sheet cut side down.
3. Roast in the oven until the shallot is soft, approximately 20 to 30 minutes.
4. Let it cool; remove the skin and the root end. Make the shallot in puree form together with the salt in a food processor.
5. In the food processor, combine mustard and puree. Add the vinegar by the tablespoon
6. While the food processor running, add the olive oil and chicken stock slowly
7. Add the chives and pepper. Adjust the salt and pepper to taste.
For the chicken barbecue and grilled onion:
1. Preheat the grill to medium-high.
2. Brush the chicken breasts and onion slices with olive oil and season with salt and pepper.
3. Grill the chicken for about 4 to 6 minutes each side, depending on the thickness until the chicken is thoroughly cooked. During the last 3 minutes of cooking, brush the chicken on all sides with the barbecue sauce. Grill the onion about 2 to 3 minutes per side, Remove the chicken and onions from the grill and place on a cutting board to rest. Cut the chicken into strips. Separate the onion slices into rings.
1. Put lettuce in a bowl and toss it with the vinaigrette. Arrange the chicken strips and grilled onion rings on top.