Bring a large pot of salted water to a rolling boil for the pasta.
Season the diced chicken generously with kosher salt, pepper, 1/2 tsp dried oregano, and dried basil.
Heat a large skillet over high heat and spray lightly with cooking spray. Add the chicken and cook, stirring occasionally, about 3–4 minutes until cooked through and no longer pink; remove the chicken from the skillet and set aside.
Meanwhile, add the spaghetti to the boiling water and cook according to package directions until al dente; reserve 1/2 cup of the pasta cooking water, then drain the pasta.
With the skillet still hot, add the 4 tsp olive oil and the chopped garlic. Sauté over high heat just until the garlic is golden, being careful not to burn it.
Add the halved grape tomatoes to the skillet, season with salt and pepper, reduce heat to medium–low, and sauté about 4–5 minutes until the tomatoes soften.
Add the drained pasta to the skillet with the tomatoes and toss well; if the mixture seems dry, add some of the reserved pasta water a tablespoon at a time until the sauce coats the pasta.
Return the cooked chicken to the skillet, add the chopped fresh basil, toss to combine, and heat through.
Serve immediately and top with grated cheese if desired.
