Heat the oil in a medium skillet over medium heat. Add the onion and garlic and cook until softened, about 3 minutes.
Add the chicken, cumin, chili powder, salt, and pepper. Cook for an additional 2 minutes.
Place one tortilla in a large nonstick skillet over medium heat. Sprinkle with one-quarter of the cheese. Top with one-quarter of the chicken mixture. Top with another one-quarter of the cheese. Place another tortilla on top.
Cook until lightly browned on both sides, about 2 minutes per side.
Repeat with remaining ingredients to make four quesadillas.