In a medium skillet over medium heat, saute the bacon until crisp. Use a slotted spoon to transfer the bacon to a paper towel-lined plate. Turn the heat off and whisk the shallots into the bacon grease. There should be about 1/4 cup of bacon grease; if it's shy of that amount, add some extra-virgin olive oil.
In a small bowl, whisk the vinegar and Dijon until emulsified. Add in the bacon grease mixture and whisk. Whisk in the salt and pepper.
To poach the eggs: Fill a nonstick skillet with about 2 inches of water and bring it to the barest simmer over medium heat; add a little vinegar if using. Crack the eggs, slipping them gently into the water one at a time, and cook until the whites are set but the yolks are still runny, 3 to 4 minutes. Using a slotted spoon, gently scoop the eggs from the water and blot dry with a paper towel.
In a large salad bowl, toss the frisee with the dressing and bacon. Divide the lettuce among 4 serving bowls and top each with an egg and a sprinkle of chives.