Heat a large saucepan over medium heat. Add oil, onion, and garlic. Cook until onions are translucent, 3 to 5 minutes. Add chicken broth, peas and carrots, thyme, parsley, salt, and black pepper and bring to a boil. Add chicken and pasta. Reduce heat to a simmer and cook until chicken is opaque throughout and pasta is tender, 5 to 10 minutes. Season with salt and pepper.
