Bring a large pot of salted water to a boil. Season the chicken with salt and pepper. Heat the olive oil in another large pot over medium-high heat. Add the chicken and cook, turning once, until browned, about 7 minutes. Move the chicken to one side of the pot.
Add the onion to the other side of the pot and cook, stirring, until just softened, about 2 minutes. Stir in the garlic; cook 30 seconds. Add the wine, olive brine and rosemary and cook, stirring everything together and scraping up any browned bits, until the liquid is mostly reduced, about 1 minute. Add the tomatoes, 1/2 cup water and a pinch of salt. Bring to a boil, reduce to a simmer and cook until the chicken is cooked through and the sauce is thickened, 8 to 10 minutes. Discard the rosemary; shred the chicken with 2 forks.
Meanwhile, add the pasta to the boiling water and cook as the label directs for al dente. Reserve 1 cup cooking water, then drain.
Add the pasta, olives and 1/2 cup cooking water to the shredded chicken mixture. Cook over medium heat, tossing, until the pasta is well coated, 1 to 2 minutes, adding more cooking water as needed to loosen. Season with salt and pepper and stir in the parsley. Divide among bowls. Drizzle with more olive oil and top with parmesan.