Start the water boiling for the pasta.
Dice the onion and sauté in olive oil over medium heat in a large sauté or sauce pan large enough so that you can add in the pasta after it has cooked.
After 2 minutes, add the garlic, stirring occasionally until the onion and garlic are soft and aromatic.
Add the diced tomatoes and salt & pepper to taste. If you have some chicken broth handy, you can add some of that too. Simmer for about 10 minutes.
Once the water is boiling, add the pasta.
While the pasta cooks, add the spinach to the sauce in small handfuls, stirring to incorporate into the sauce. Continue to simmer, and add the shredded chicken, stirring occasionally.
Before draining the pasta, reserve some of the pasta water, about a cup. Drain the pasta and add it to the sauce while it continues to cook, mixing the pasta in so it can absorb the flavor of the sauce. You may need to add some pasta water to help it along. Cook for another 3-5 minutes.
Serve in large bowls topped with shredded cheese to taste.