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Preheat oven to 375 degrees.
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Place Chicken Broth ingredients in a large pot and cover with water; bring to a boil, then reduce heat to low and simmer, covered, while you roast chicken for the soup.
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Meanwhile, rub chicken breast with olive oil and season with salt and pepper. Place on baking sheet lined with aluminum foil; roast 25-30 minutes until just cooked through. Remove chicken from oven; let cool slightly; remove meat from bones and put bones and skin in soup pot. Shred cooked chicken breast.
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Let soup simmer for 2-3 hours. Alternatively, you can cook soup in the pressure cooker for 1 hour. When done, strain soup and return to pot. Add carrots, celery, onion and potatoes; cook until vegetables are tender, about 30 minutes. Add shredded chicken breast to soup and warm through.