Cook the spaghetti according to the package instructions in a large pot with salted water. Drain and set aside.
In a skillet, heat olive oil over medium heat. Add the cubed chicken and cook until browned and cooked through, about 5-7 minutes.
Stir in the chopped onion, red, and green bell peppers. Sauté for an additional 5 minutes until the vegetables are tender.
Add the minced garlic, diced tomatoes (with their juice), tomato sauce, oregano, basil, salt, and black pepper to the skillet. Stir well and let simmer for 10 minutes.
Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the cooked spaghetti with the chicken and vegetable mixture. Stir well to coat the spaghetti evenly.
Transfer the spaghetti mixture to a 9x13-inch baking dish. Top with shredded Monterey Jack cheese.
Bake in the preheated oven for 15-20 minutes, or until the cheese is melted and bubbly.
Remove from the oven and sprinkle with chopped cilantro (if using) before serving hot.