Place the potatoes in a saucepan of very salty water and bring to the boil. Cook for about 10 minutes until tender when pierced with a small, sharp knife. Remove with a slotted spoon and set aside until cool enough to handle.
Cut the potatoes into bite-size pieces.
Return the water to the boil. Cook the beans for 3 minutes or until tender. Drain and refresh under cold running water.
For the dressing, finely chop the eschalot with 2 of the anchovies. Whisk the vinegar and mustard in a bowl, then whisk in the oil a little at a time until emulsified.
Stir in the eschalot mixture until combined. Season to taste with salt and pepper.
Remove the chicken meat and skin from the carcass, and tear into bite-size pieces. Arrange the chicken, olives, tomatoes and remaining anchovies on a large platter in individual piles and season well with salt and pepper. Drizzle with the dressing and serve.
