Cook the bacon in a medium skillet over medium heat until crisp, about 8 minutes. Transfer to a paper towel-lined plate. Transfer 1 tablespoon of the bacon drippings to a small bowl.
Add the oil, vinegar, 1/4 teaspoon salt, and 1/4 teaspoon pepper to the bacon drippings. Whisk and set aside.
Shred the chicken meat, using your fingers or a fork, discarding the skin and bones.
Combine the lettuce, cheese, tomatoes, avocado, onion, and chicken in a large bowl.
Crumble the bacon over the salad and serve with the vinaigrette.
Substitution: This classic dish can be made with almost any kind of lettuce. If you like a crunchier salad, use romaine. If you prefer tender greens, try Boston or Bibb. For a hit of pepperiness, opt for arugula or add a few leaves of radicchio or endive to your standard mix.