Bring a large pot of cold water to a boil over high heat and salt it generously. Add the pasta and boil, stirring occasionally, until al dente, about 8 minutes. Drain.
Meanwhile, heat the olive oil in a large saucepan over medium heat. Add the onion, garlic, carrot, celery, and salt; cook until tender, about 8 minutes. Add the chicken, bay leaf, thyme, and broth to the vegetables, cover, and simmer for 10 minutes.
Add the pasta to the soup just before serving. Ladle into warm bowls and serve. Soup can be made in advance and frozen, just omit the pasta and add when serving.
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