In a large casserole dish, toss the sliced onions with the cooking oil. Place in the oven and bake for about 20-25 minutes, stirring halfway through until the onions become tender and golden brown.
While the onions are cooking, mix the shredded chicken with the mayonnaise, sour cream, chopped garlic, salt, and black pepper in a large bowl.
Once the onions are ready, take them out of the oven and combine them with the chicken mixture directly in the casserole dish.
Spread the provolone cheese slices evenly over the top of the chicken and onion mixture.
Lower the oven temperature to 375°F and bake for another 15-20 minutes, or until the casserole is hot and the cheese is bubbly and melted.
Let it cool for a few minutes before serving. Enjoy!