In a sauté pan or skillet large enough to hold all of the pasta after it has been cooked, warm the olive oil over medium-high heat for 1 minute. Add the chicken and sauté, stirring, until it is cooked through. Lower the heat to medium and add the roasted red peppers, oregano, rosemary, and chicken broth.
In a large pot of boiling salted water, cook the pasta according to package directions for al dente. Drain the pasta and add it to the sauté pan with the chicken. Stir to combine. Add freshly ground pepper. Serve in large pasta bowls, with parmesan cheese on the side.