Season the chicken generously with salt and pepper on all sides. Set aside, at room temperature while you cook the bacon. Note: A 15-minute sit at room temperature will make the chicken cook more evenly, helping you avoid a brown outside with a raw, undercooked inside.
Cook the bacon in a large skillet over medium heat, flipping occasionally, until crispy – about 8-10 minutes. Use tongs to transfer the cooked bacon to a paper towel-lined plate to rest, leaving behind most of the rendered bacon fat in the skillet.
Preheat your oven to 350F, then place the chicken breasts, skin side down, into the skillet with the bacon fat. Cook over medium heat for 5-7 minutes to get some color on the skin then transfer the skillet to the pre-heated oven to finish cooking – about 15-20 minutes. Rest the cooked chicken under a sheet of foil for 5 minutes before slicing it off the bone and roughly chopping into bite-sized pieces.
In the meantime, bring a small pot of water to a boil. Gently place the eggs into the water. Set a timer for 8 minutes for soft, jammy eggs or 10 minutes for hard boiled. When the timer goes off remove the eggs from the water and places them directly into a bowl of ice water. As soon as the eggs are cool enough to handle, but still warm, carefully peel off the shell. Give them a final rinse under water to remove any unseen bits of shell then slice each egg in half and season with salt and pepper.
While the eggs are boiling whisk together the dressing ingredients starting with the mustard, garlic and vinegar then, while whisking begin to slowly stream in the olive oil until fully combined, set aside.
To assemble the salad: in a large mixing bowl toss the lettuce, tomatoes, shallot and chives together with the vinaigrette, use just enough to lightly coat each leaf you may not need all of it. Arrange the salad on individual pates or one large platter. Scatter the chicken, bacon, eggs and blue cheese around evenly. Season with salt and pepper – serve immediately.