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Heat 2 tsp oil in a soup pot over medium-high heat. Season chicken with salt and add to pot until just cooked through (~5 min). Transfer chicken to dish and set aside
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Add remaining 2 tsp oil, onion, celery, carrot, and thyme and cook over med-high het until tender (~5 min)
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Add 5 cups broth and bring to a boil
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Add orzo and simmer until tender (~8 min). Turn the heat down to low to maintain heat without boiling
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Warm 1 cup broth in small saucepan until hot but not boiling. In medium bowl, whisk eggs while gradually adding lemon juice
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Gradually whisk in the hot broth to the egg-lemon mixture
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Add mixture to soup, stirring well until soup thickens
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Add cooked chicken and season with salt and pepper