In a large skillet, fry the bacon over medium heat until lightly golden but still soft; drain. Pour out the excess fat, reserving the skillet.
Season the chicken with salt and pepper. Wrap two strips of bacon around each chicken breast and secure with toothpicks.
Heat the reserved skillet over medium heat. Add the chicken, cover and cook, turning once, until golden, 5 to 6 minutes on each side. Transfer to a cutting board and let rest for 5 minutes; discard the toothpicks.
Meanwhile, in a large bowl, whisk together the lime juice and olive oil. Add the lettuce, tomatoes, avocados, pepper jack and chives, season with salt and pepper and toss. Divide among serving plates and top with the chicken.