In a big soup pot, heat the oil over medium-high heat. Add the onion and cook, stirring, until softened, 6 to 8 minutes. Add the carrots, celery, garlic, thyme, 1 tablespoon salt, and 1 teaspoon pepper and cook, stirring, until the carrots soften slightly, about 5 minutes. Add the bay leaf and chicken broth and bring to a boil. Reduce the heat and simmer for 45 minutes to meld the flavors.
Stir in the noodles and chicken and simmer for 5 to 10 minutes longer. Season to taste with more salt and pepper and discard the bay leaf. Serve with buttered saltines, if you want to be like me and my dad.