Heat 1 Tablespoon oil in a skillet over medium heat.
Add onion and cook until soft, about 3 minutes.
Stir in garlic, chili powder, oregano, and cumin. Cook for 30 seconds.
Add shredded chicken, salt, pepper, and green chilies. Cook for 3 minutes. Remove from heat.
Place ¼ cup chicken mixture in the center of each tortilla.
Sprinkle with cheese.
Fold sides of tortilla over filling, then roll up tightly.
Heat remaining oil in a large skillet over medium-high heat.
Fry chimichangas seam side down until golden brown, about 2 minutes per side.
Drain on paper towels.
Serve with desired toppings.