Heat the oil in a medium saucepan over medium heat. Add the onion, celery, garlic, chili powder, and cumin, and cook until the onion softens, about 5 minutes. Add the chicken broth, bring to a boil, reduce the heat slightly, and simmer, uncovered, for 10 minutes. Add the green chiles, posole, tomatoes, and oregano and cook for another 5 minutes.
Pull the saucepan from the heat and stir in the chicken, cilantro leaves, and lime juice. Season, to taste, with salt and pepper. Serve hot.
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