Preheat oven to 425°F. Line a 9x13-inch (or larger) baking sheet with parchment paper.
Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Add the chopped onion and cook until softened, about 3 minutes.
Stir in the chicken, salsa, taco seasoning, salt, and pepper. Cook for 2-3 minutes, then remove from heat and stir in the lime juice.
Wrap tortillas in a damp paper towel and microwave for 30 seconds to make them pliable. (This helps prevent cracking when folding.)
Spoon the chicken mixture onto one half of each tortilla. Sprinkle with cheese, fold over, and arrange on the prepared baking sheet(s).
Lightly brush the tops of the tortillas with the remaining olive oil.
Bake for 12-15 minutes, or until golden brown and crispy.
Serve warm with your favorite toppings (e.g., sour cream, cilantro, shredded lettuce, extra salsa)