Preheat your oven to 400 degrees. Line a rimmed baking sheet with aluminum foil. Place a wire cooling rack in the tray. Spray it liberally with cooking spray. Set aside.
In a large bowl, combine the chicken, cheese, taco seasoning, and green chiles.
Add about 2 tablespoons of the chicken mixture to each corn tortilla. With the seam side up, thread a long toothpick to hold the tortilla closed. Brush the tortillas liberally with the vegetable oil. (See my note about spraying with vegetable oil.)
Place the rolled taquitos on the wire rack. Bake for 10 to 15 minutes or until the tortillas are golden brown. Remove from the oven, take out toothpicks, add toppings, and enjoy while warm.
If you want to make this recipe just a little easier you could spray both sides of the taquitos with cooking spray, rather than brushing them with oil. This is much faster, but the taquitos don't get quite as crisp.