Combine chicken, olives, almonds, and enough of the enchilada sauce to moisten (about 1/3 cup).
Use tongs to dip the tortillas into medium-hot oil. Fry tortillas just a few seconds, until they bubble and are limp--do not fry crisp.
Dip fried tortilla into heated enchilada sauce as soon as it comes out of the hot fat. A cake pan just larger than the tortilla is an ideal utensil.
Lay sauce-dipped tortilla out on a board or pan. (This part of enchilada making is admittedly slightly messy, but well worth the trouble.) Generously spoon the chicken filling in the center of the tortilla.
Turn tortilla over the filling, roll, and place (with the flap pointing down) in baking pan. Fry, dip, fill, and roll remaining tortillas. Ladle additional enchilada sauce over enchiladas and top with cheddar. Place enchiladas in a moderate oven (350°) for 15 to 20 minutes--or until thoroughly heated. Mix cold sour cream with onions and serve as a sauce.