Fill a large pasta pot with water and place it over high heat. Once the water comes up to a boil, salt it and drop in the pasta. Cook the pasta to al dente according to package directions. Before draining the pasta, reserve a mugful of starchy cooking water, then drain and reserve.
While the water is coming up to a boil, place a large skillet over high heat with 3 turns of the pan of EVOO, about 3 tablespoons. Season the chicken pieces with the poultry seasoning, salt and pepper then add it to the preheated skillet. Cook the chicken until golden brown and cooked through, 4 minutes per side.
Once the chicken is brown, add the onions to the pan, and cook until softened, about 5 minutes. Add garlic, cook a couple of minutes more then add the tomatoes and cover the pan with a lid. Cook, stirring occasionally, until the tomatoes burst open and begin to release their juices, about 6-7 minutes (if they havent started to burst open by that time, mash them lightly with a potato masher or wooden spoon). Season the mixture with salt and pepper.
Add the drained pasta and reserved starchy cooking water to the skillet with the chicken and tomatoes, and toss over the heat until combined, about 1 minute. Remove the pan from the heat and stir in the basil, arugula, and cheese. Serve.