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Heat oil in a large skillet over medium heat. Add onion and garlic and saute 2 minutes. Add chicken and saute 5 minutes, until golden brown and cooked through. Remove half of the chicken and reserve for another use.
Arrange 4 tortillas on a flat surface. Top each tortilla with an equal amount of chicken mixture. Roll up tortillas and place side by side in a shallow baking dish. Top tortillas with shredded cheese (1/3 cup per tortilla).