Bring a large pot of water to a boil. Add salt, then add the pasta, cook until al dente and drain.
Heat a large, deep skillet over high heat. Add the EVOO, 3 turns of the pan. Add the chicken and cook over high heat until lightly browned. Sprinkle the thyme, zest and red pepper flakes over the chicken and stir to combine. Add the garlic, peppers and onion and season with salt and pepper. Cook for 5 to 6 minutes, stirring now and then, until the veggies soften. Add the wine and scrape up the tasty bits from the bottom of the pan. Stir in the broth and tomatoes and bring to a bubble. Simmer the sauce for 10 minutes.
Combine with the chicken, peppers and onion and a little grated cheese. Serve at once and pass around extra cheese at the table.