Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente. Drain, reserving 1 cup of the pasta cooking water and the pot.
While the pasta is working, in a large skillet, heat the EVOO, 2 turns of the pan, over medium-high heat. Season the chicken with salt and pepper and add to the skillet. Sprinkle the rosemary on top and cook the chicken until crispy and brown, 8 to 10 minutes. Transfer to a platter.
Whisk the balsamic vinegar and marmalade into the skillet, scraping up the browned bits from the bottom of the pan. Lower the heat and simmer for 1 minute. Return the chicken to the pan and coat with the sauce. Remove the pan from the heat and stir in the arugula.
In the pasta pot, melt the butter over medium-low heat. Add the sage and cook until fragrant, about 5 minutes. Add the pasta and pasta water and toss. Add the 1/2 cup grated cheese and season with salt. Sprinkle the pecans on the chicken and serve with the pasta and a little extra cheese.