Put the pot on the stove and turn the heat to medium. When it is hot, carefully add the oil.
Add the onion, celery, carrots, and thyme, and cook until the vegetables are starting to soften, stirring occasionally, 10-15 minutes.
Add the chicken broth, turn the heat up to high and bring to a boil. Turn the heat down to low, and cook, uncovered, until the vegetables are tender and no longer float on the top, about 30 minutes.
Add the alphabet-shaped pasta and cook until tender, about 8 minutes (or follow the cooking time on the package directions).
Add the chicken, if using, and stir until heated throughout, about 1 minute. Taste the soup and add a pinch of salt if you think it needs it. Serve right away or cover and refrigerate up to 3 days.