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Preheat oven to 350 degrees.
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In a large stock pot, heat olive oil over medium-high heat.
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Add garlic and rosemary, sauté until fragrant (about 2 minutes).
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Sear chicken breasts in oil just until browned on each side.
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Place chicken breasts in oven, bake about 30 minutes, until no longer pink in the middle. While the chicken is cooking, finish the rest of the soup.
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Add celery and onion to pot, sauté until just softened, 6-8 minutes.
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Add chicken stock and bring to a boil.
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Add chopped potatoes, cover. Maintain a low boil until potatoes are soft.
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When chicken is done, remove from oven, let cool slightly then shred or chop.
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Remove 2 cups of soup from pot and purée in a food processor, then return to pot. This will thicken the soup.
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Add shredded chicken and season with salt and pepper to taste.
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The soup can stay on the stove over low heat until ready to serve but the potatoes will continue to soften.