Dry fry the bacon lardons in a frying pan over a medium heat until crisp - this will take about 10 minutes. Drain on kitchen paper and keep warm.
Meanwhile, in a small bowl, whisk together the vinegar and mustard. Slowly add the oil, continuing to whisk until the mixture thickens. Set aside.
Half-fill a large pan with water and bring to a gentle simmer. Break each egg into a ramekin, keeping the yolks intact. One at a time, pour the eggs into the simmering water and gently spin the water around each egg with a slotted spoon to allow the white to fold over itself. Cook until the whites are just firm – about 4-6 minutes for a runny yolk; longer if you prefer them harder. Remove with a slotted spoon and drain on kitchen paper; season with freshly ground black pepper.
Toss the salad in a bowl with the vinaigrette and bacon. Divide between 4 plates, top each with a poached egg and sprinkle with the chives to serve.