Preheat oven to 350. Combine chicken, onions, and 1 cup of jack cheese.
Heat about 1/4 inch of oil in a small skillet over medium heat. Using tongs, dip each tortilla into the oil for 5 seconds per side; drain on paper towels.
Assemble as follows: Dip tortilla in tomatillo salsa. Place 3-4 tablespoons of chicken mixture in each tortilla and roll tortilla up; place seam-side down in a large baking dish. (I use one 9x13 pan and one 9x9 pan to freeze for later!) Leave space between each enchilada. Repeat until all mixture is used.
Pour the rest of the tomatillo salsa over all the enchiladas and sprinkle the jack on top.
Cover loosely with foil and bake for 20-25 minutes.
Garnish with a Monterey Jack cheese, a dollop of sour cream, and a few olive slices.