To prepare the vinaigrette, combine the first 6 ingredients, and stir with a whisk. Set aside.
To prepare the quesadillas, combine the goat cheese and the next 5 ingredients (goat cheese through 1/4 teaspoon black pepper) in a small bowl. Spread 2 tablespoons of the goat cheese mixture evenly over each tortilla. Arrange 1 cup chopped chicken over the goat cheese mixture on each of 2 tortillas, and top with the remaining tortillas.
Heat a large nonstick skillet coated with cooking spray over medium heat. Cook the quesadillas for 4 minutes on each side or until golden brown. Remove the quesadillas from the skillet, and cut each quesadilla into 8 wedges. Combine the vinaigrette with the salad greens, and toss well. Arrange 2 cups salad on each of 4 plates, and top each serving with 4 quesadilla wedges.