Bring a large pot of lightly salted water to a boil. Cook spaghetti in boiling water, stirring occasionally, until tender yet firm to the bite, about 12 minutes. Drain.

Preheat the oven to 350 degrees F (175 degrees C).

Heat olive oil in an oven-proof skillet over medium heat; cook and stir garlic until fragrant, about 1 minute. Add onion; cook and stir until onion begins to soften, about 2 minutes. Add chicken; cook and stir until chicken is no longer pink in the center, about 5 minutes.

Mix cream of mushroom soup and diced tomatoes with green chile peppers into chicken mixture. Mix spaghetti into chicken mixture and top with Colby-Monterey Jack cheese.

Place the skillet in the preheated oven and bake until cheese is melted and slightly brown, 15 to 20 minutes.