Preheat your skillet over medium heat.
In a bowl, mix the shredded chicken, mozzarella, Parmesan, minced garlic, and sour cream together.
Place a tortilla on a flat surface and spoon a generous amount of the chicken mixture in the center.
Fold in the sides of the tortilla and then roll it tightly from the bottom to the top.
Drizzle olive oil in the skillet and place the wrap seam-side down.
Cook each wrap for about 3-4 minutes on each side until golden brown and the cheese is melted.
Remove from the skillet and allow to cool for a minute before slicing in half.
Serve warm with your favorite dipping sauce.