Put the chicken breasts in a small dish, season with salt and pepper and drizzle with olive oil. Cover with cling film and leave to marinate for 15–20 minutes.
Meanwhile, soft-boil the quail eggs. Fill a small saucepan with water and bring to the boil. Add the vinegar to the water, as this will make the eggs easier to shell after cooking. Place the eggs in a ladle, then slowly and carefully slide them into the water so that you don’t break the shells. Cook for 4 minutes, drain and place the eggs under running cold water. When cool enough to handle, shell the eggs, cut in half and set aside.
Meanwhile, put the mayonnaise, tarragon and lemon juice in a large serving bowl, season with salt and pepper and mix well. Add the lettuce and mix.
Remove the chicken from the oven and cut it into thick slices while it is still warm. Arrange the slices on top of the salad and top with the quail eggs and finally the croûtons. Serve warm.