Wash the potatoes, and boil them in their skins for about 45 minutes.
Cook the chicken in a pan together with the celery stick, the carrot, 3 or 4 peppercorns, and salt to taste. Boil for 15 minutes.
While you're cooking the potatoes and the chicken, finely chop the onion, and put it in a bowl with some water to take away some of the bite.
Finely chop the red chilli into pieces about the same size as the onion, and set it aside in a bowl.
Hard boil 2 eggs to add to the dish for decoration.
Slice the avocado thinly, and sprinkle with the lemon or lime juice to stop it from going brown. Set this aside too.
Cut the carrot into pieces, and reserve this as well.
When the potatoes are cooked, peel them while they're still warm (it's easier this way), and then grate them so that you can make a purée. Set aside, and keep them at room temperature so that the purée is easier to make.
Next, pull the chicken breasts apart into strips with your fingers.
At this point it's time to make the purée with the grated potato, the two spoonfuls of yellow chilli paste, a little salt and a drizzle of oil (not too much, you don't want an oily texture). Once all the ingredients are well mixed, set aside.
In another bowl prepare the chicken filling, using the chicken, the chopped onion, carrot and red ají chilli. Add a couple of spoonfuls of mayonnaise to the mix, and blend the ingredients together well. Check the seasoning, and if necessary add a bit more salt. Reserve when mixed.