Heat olive oil in a large pot or deep skillet over medium-high heat.
Add the chicken pieces and cook for 5-6 minutes until browned on all sides but not fully cooked through. Remove chicken from the pot and set aside.
In the same pot, add the diced onion and cook for 3-4 minutes until softened.
Add the minced garlic and cook for 1 minute until fragrant.
Return the chicken to the pot. Sprinkle in the dried Italian seasoning, salt, and black pepper. Stir to combine.
Pour in the chicken broth, diced tomatoes with their juice, and add the uncooked penne pasta. Stir well to combine all ingredients.
Bring the mixture to a boil, then reduce heat to medium-low. Cover and simmer for 15 minutes, stirring occasionally to prevent sticking.
After 15 minutes, check the pasta for doneness. If needed, cook uncovered for an additional 3-5 minutes until pasta is tender and the sauce has thickened.
Stir in the fresh baby spinach leaves and cook for 1-2 minutes until wilted.
Remove the pot from heat and stir in the grated Parmesan cheese until melted and well combined.
Serve hot immediately.