How to Make It
In a skillet, heat 1 tablespoon of the oil. Add the leeks and a pinch of salt; cook over moderate heat until softened. Add 2 tablespoons of water, cover and cook over low heat for 4 minutes. Remove from the heat.
In a small saucepan, combine the sugar with 1 tablespoon of water and simmer over moderate heat until syrupy, 2 minutes. Add the preserved lemon and simmer for 1 minute; add to the leeks and keep warm.
In a bowl, whisk the vinegar, chives, dill and tarragon with 2 tablespoons of the olive oil. Season with salt and pepper.
In a skillet, heat the remaining 1 tablespoon of oil. Season the chicken with salt and pepper and add to the skillet. Cook over moderately high heat until golden, 3 minutes. Reduce the heat to moderate and cook for 2 minutes longer. Turn the breasts and cook until just white throughout, 4 minutes.
Spoon the leeks onto plates. Top with the chicken. Drizzle with the vinaigrette, garnish with the walnuts and serve.