Rinse chicken parts, remove and discard skin. Place in a pan of water and gently boil until cooked through, about 15 minutes. Drain and allow to cool for a few minutes. With a fork or fingers, shred chicken.
Mix together the shredded chicken, salsa, and sour cream. Season with salt and pepper to taste. If mixture is watery, drain off the excess liquid.
Warm tortillas in the oven or microwave and keep them warm wrapped in a clean kitchen towel while you work.
In a large skillet, heat ½ inch of oil to 350 degrees (medium hot). While the oil is heating, make chimichangas one at a time. In the center of each tortilla, drop 1/12 of the chicken mixture, then heap two tablespoons of cheese along the side of the chicken mixture. Roll up like a burrito, making sure all the filling is completely folded inside. Set aside seam side down while you make the rest. At this point, chimichangas may be individually wrapped in plastic wrap or foil and refrigerated for a day or frozen for a month to cook later. If freezing, allow to thaw completely before frying, and pat dry with a paper towel before frying.
Using tongs, gently place 2 -3 chimichangas in hot oil, seam side down, lightly pressing down with a spatula if they start to unroll. Cook on one side till golden brown, then turn with tongs and cook the other side till golden brown. Try to only turn them once so they don’t absorb too much oil. Place cooked chimichangas on a paper-towel lined platter in a warm oven (170 degrees) while you cook the rest.
Note: Do not try to save a step and mix in the shredded cheese with the chicken. It will be much more satisfying to bite into them and get that pocket of hot, melted cheese.