Bring a medium saucepan of water to a boil. Add chicken; cook at a bare simmer until it is cooked through, about 15 minutes. Transfer to a plate, and cut into 1/2-inch cubes; set aside.
Place eggs in a small saucepan; fill with enough cold water to cover by 1 inch. Bring to a boil over medium-high heat; turn off heat. Cover; let stand 11 to 12 minutes. Transfer to a small bowl, and cover with cold water; let cool, and peel. Slice eggs in half lengthwise. Discard one yolk, and pass the other through a fine sieve into a small bowl; set aside. Slice each egg white into six wedges; set aside.
Cook bacon in a medium saute pan over medium-low heat until browned and fat is rendered, turning once, about 3 minutes per side. Transfer to drain on paper towels. Let cool; roughly chop.
Spread lettuce on a serving platter. Arrange chicken, eggs, bacon, watercress, tomatoes, avocado, parsley, and chives in separate rows.
Make the vinaigrette: In a small bowl, whisk together cheese, vinegar, and mustard. Slowly whisk in the oil. Season with pepper. Drizzle vinaigrette over salad, and serve immediately.