Bring a large pot of water to a boil and add salt. Cook the pasta in the boiling water according to the package directions; do not overcook. Drain and rinse in cold water to cool. Toss in 1 tablespoon of the olive oil and set aside.
Put the chicken pieces in a large pot or Dutch oven and cover in the chicken broth. Bring to a boil, lower to a simmer and cook, covered, for 45 to 50 minutes.
Remove the chicken pieces from the pot, shred the meat and set aside. Discard the bones and skin. Skim the fat from the stock, then strain the stock and set aside.
In a new pot, add the remaining 1 tablespoon olive oil and saute the bell peppers, celery, jalapenos, onion and oregano over medium heat until the vegetables are tender and golden brown, about 10 minutes. Add the tomatoes with their liquid and the reserved chicken stock and shredded chicken. Bring to a boil, then reduce to a simmer. Add the cooked pasta and cream and stir to combine. Turn off the heat.
Serve with lots of Parmesan on the top--the more the better--and crusty Italian bread is good too.