Rinse chicken and pat dry. Peel and halve the onion. Clean and wash carrots and cut into bite-sized pieces.
Put the vegetables in a pot with the bay leaf and bring to a boil, covered with water and simmer for a quarter of an hour. Add salt and let the chicken breasts simmer in it for a quarter of an hour on a low heat.
Mix yolks with garlic and lemon juice. Slowly drizzle in olive oil, then continue blending until a mayonnaise is formed.
Cut the chicken breasts into thin slices, drizzle with a little sauce, pepper and serve garnished with plucked basil.