Cook bacon in a skillet over medium heat, turning occasionally, until crisp. Transfer bacon to a plate lined with paper towels, reserving drippings in skillet.
Pour drippings into a small bowl; set aside to cool slightly.
Set bacon aside. Reserve 1 bacon slice. Roughly chop remaining 3 bacon slices, and toss in a large bowl with lettuce, eggs, chicken, tomatoes, avocado, and cheese.
Crumble reserved bacon slice into a food processor. Add garlic, salt, pepper, and sugar; pulse until finely chopped, about 5 times.
Add reserved drippings, olive oil, and vinegar; process until blended.