Salt and pepper the chicken pieces and prick them in several places with a fork. Puree the orange juice, achiote paste, garlic and spices and pour this mixture from the blender into a large bowl. Place the chicken pieces in this marinade and put them aside while you make the sauce.
Put the chiles, in a saucepan with the 3 1/2 cups water and bring them to a boil. When they have reached the boiling point, turn down the heat and let them simmer, covered, for about twenty minutes. Puree them in a blender with the onion, tomato and salt to taste. Strain back into saucepan and simmer the sauce for about 10 minutes.
If using mixiotes, soak them for 5-10 minutes until pliable. Into each mixiote or plastic baggie, put one avocado leaf, a piece of marinated chicken, a few potatoes and carrots, and a few spoonfuls of sauce. Tie each package with twine or string and, if using plastic baggies, wrap each bundle in foil, sealing well.
Put water into a large pot with a rack (or, if you have one, a tamale steamer) and place the mixiotes on the rack. Cover tightly and steam 1 1/2 -2 hours. Thighs will take longer than breasts, so if you're using breasts, check one package after the first 1 1/2 hours. To serve, unwrap the foil if you used it, and place each mixiote in a soup or stew bowl. Each person unties and unwraps his own mixiote, letting the liquid flow into the bowl with the chicken. Serve with sliced avocado and tortillas. The word mixiotes refers to one of the most delectable dishes within the wide spectrum of Mexican cooking, as well as the wrapping used to contain these steamed individual meat stews.
This wrapping, also known as a mixiote, is the outermost layer of a maguey leaf, called a penca. If you don't live near a Mexican market where you can buy mixiotes, you can use papel para mixiotes, which are simply plastic baggies, a commonly used substitute. If you use plastic baggies, wrap each bagged bundle in foil before steaming.