Wash the lettuce. Drain in a colander and shake out excess moisture or dry the lettuce in a salad spinner. Wrap the lettuce in paper towels, put in a plastic bag, and refrigerate for 1 to 2 hours.
In a small bowl, combine 1 tbsp of the vinegar, the oil, mustard, and salt and freshly ground pepper to taste. Mix the vinaigrette well and set aside.
In a skillet, sauté the bacon, and when it becomes crisp, remove it with a slotted spoon to drain on paper towels. Sauté the chicken livers in the bacon fat until they just turn from pink and remove them with a slotted spoon to drain on paper towels.
Over moderate heat, deglaze the pan with the remaining 2 tablespoons vinegar, reduce it slightly, stir in the vinaigrette, and remove from the heat.
In a large salad bowl, mix the salad greens together and add the warm dressing. Mix well and garnish with the onion slices, croutons, chicken livers, bacon, and chives. Serve immediately.