Put the oil in a large, deep skillet over medium-high heat. When it’s hot, sprinkle the chicken with salt and pepper and add it to the pan, skin side down. Cook, turning the pieces as necessary, until the chicken is browned on both sides, about 10 minutes. Remove the chicken from the pan.
Turn the heat down to medium. Add the onions and garlic, sprinkle with salt and pepper, and cook, stirring occasionally, until soft, about 5 minutes. Add all but 1 cup of the zucchini and stir to coat with the oil. Add the wine, stock, pasta, and reserved chicken.
Bring to a boil, scraping up any bits that might be stuck to the bottom of the pan. Reduce the heat so the mixture bubbles enthusiastically and cook, stirring frequently and adding more liquid as needed to keep the mixture saucy, until the pasta just begins to get tender, no more than 10 minutes. Stir in the remaining zucchini and cook until it softens a little and the pasta is ready but not mushy, another 3 minutes. Stir in the dill, and Parmesan if you’re using it. Taste, adjust the seasoning, and serve.