Preheat the oven to 350°F (175°C). Grease a 9x13-inch baking dish.
In a large skillet, heat the olive oil over medium heat. Add the chicken pieces and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the chopped onion and minced garlic. Sauté until softened and fragrant, about 3-4 minutes.
Stir in the condensed cream of chicken soup and chicken broth. Cook, stirring constantly, until the mixture is smooth and heated through.
Add the sour cream, shredded Monterey Jack cheese, and shredded cheddar cheese to the skillet. Stir until the cheeses are melted and the sauce is creamy.
Stir in the diced tomatoes and green chilies, paprika, dried oregano, salt, and pepper. Mix well.
Add the cooked chicken and cooked spaghetti to the skillet, tossing to coat everything evenly with the sauce.
Transfer the mixture to the greased baking dish and spread it out evenly.
Bake in the preheated oven for 20-25 minutes, or until the top is golden and bubbly.
Remove from the oven and let cool slightly before serving.
Garnish with chopped fresh parsley and enjoy your Monterey Chicken Spaghetti!