Heat a large skillet over medium-high heat. Add 1 T. of the olive oil; heat 1 minute. Add the chicken; cook, stirring and breaking up pieces, until lightly browned, about 6 minutes. Season with 1/2 teaspoons of the salt and pepper to taste. Transfer chicken with a slotted spoon to a colander to drain; set aside.
Heat the remaining 2 T. of olive oil in the same skillet over medium heat. Add the onion, carrots and celery; cook, stirring, until they just start to color, 6 minutes. Add the garlic; cook 1 minute. Stir in the tomato paste; cook until blended and fragrant, 3-4 minutes.
Stir in the wine. Cook, stirring occasionally, until almost all the liquid has evaporated, 5-7 minutes. Add the tomatoes; cook 3 minutes. Add the broth, cooked chicken, oregano, thyme, remaining 1/2 teaspoons of salt and pepper to taste. Reduce heat to a simmer. Cook, stirring occasionally, until the sauce has thickened slightly, about 30 minutes.
Meanwhile heat a large pot of salted water to a boil. Add the rigatoni; cook until al dente according to package directions.
Stir the basil and red pepper flakes into the sauce; adjust the seasoning. Drain pasta; toss with the sauce in a large serving bowl.