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Bring chicken, water, and 1 tablespoon salt to a boil in a large stockpot. Skim foam. Add onions, celery, and garlic. Reduce heat. Simmer, partially covered, for 30 minutes.
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Remove breast, and set aside. Add carrots. Simmer, partially covered, for 40 minutes.
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Remove remaining chicken; discard back and wings. Let cool slightly. Remove meat from bones, and cut into bite-size pieces.
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Stir in desired amount of chicken; reserve the rest for another use. Skim fat. Season with salt.
