Wash and quarter the potatoes. Heat 1 tablespoon of oil in a frying pan and fry the potatoes for about 15 minutes over medium heat, turning them over. Season with salt and pepper. In the meantime, cut the avocado flesh into coarse pieces, sprinkle with some lemon juice and mash coarsely with a blender. Add 1 tablespoon of olive oil.
Season to taste with salt, coloured pepper and remaining lemon juice. Wash the chicken fillets, dab dry and season with salt and pepper. Heat the rest of the oil in a frying pan and fry the chicken fillets for about 12 minutes, turning them over. In the meantime, finely dice the shallots. Add half of the diced shallots to the avocado cream. Cut the tomatoes into quarters and remove the seeds. Cut the quarters into medium-sized cubes. Wash the parsley, dab dry and cut the leaves, except some for garnishing, from the stalks and cut into fine strips. Dice tomatoes, mix remaining shallots, parsley and remaining olive oil. Season with salt and pepper.
Cut the tomatoes into quarters and remove the seeds. Cut the quarters into medium-sized cubes. Wash the parsley, dab dry and cut the leaves, except some for garnishing, from the stalks and cut into fine strips. Dice tomatoes, mix remaining shallots, parsley and remaining olive oil. Season with salt and pepper. Cut the chicken fillets open and arrange on plates with potatoes, avocado cream and the tomatoes. Garnish with remaining parsley