In a large pot of boiling salted water, cook the spaghetti according to the package directions until al dente. Drain and set aside.
In a large skillet, heat 1 tablespoon of olive oil over medium-high heat. Season the chicken pieces with Italian seasoning, salt, and pepper. Add the chicken to the skillet and cook for about 5-7 minutes, or until golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the remaining tablespoon of olive oil. Sauté the minced onion and garlic until the onion becomes translucent, about 3-4 minutes. If using, stir in the anchovy paste and cook for another minute to incorporate.
Stir in the capers and kalamata olives, cooking for another 2 minutes. Then, pour in the marinara sauce, allowing it to simmer for about 5 minutes to meld the flavors together.
Return the cooked chicken to the skillet, and stir to coat it in the sauce. Add the cooked spaghetti and toss everything together until the pasta is well coated and heated through.
Remove the skillet from heat and stir in the chopped fresh basil. Serve the Pasta Puttanesca with Chicken hot, garnished with extra basil if desired.