Preheat the oven to 425℉.
To a blender, add the avocado, lime juice, cilantro, sour cream, garlic powder, salt, and pepper. Blend until smooth.
In a medium size bowl, toss the chicken in half of the avocado crema mixture.
Brush the bottom of a baking sheet with 1 tablespoon of olive oil.
Place two tortillas in the center of the sheet, then drape two tortillas on each side, one on the bottom, and one on the top, overlapping them with the tortillas in the center of the baking sheet.
Add a layer of cheese on top of the tortillas. Spread the chicken mixture on top, then add the remaining cheese on top of the chicken.
Place two tortillas on top of the fillings (similar to the bottom of the pan) and start to fold the tortillas from the bottom over top of the mixture until everything is enclosed inside.
Brush the top of the tortillas with 1-2 tablespoons of olive oil until lightly coated, then place another baking sheet on top of the folded tortillas (the quesadilla will be sandwiched in between the baking sheets).
Bake for 20 minutes. Remove the top baking sheet and bake for an additional 5-10 minutes until the top of the tortillas is browned.
Let cool slightly, slice, serve alongside remaining avocado crema, and enjoy!