Heat 1/2 tablespoon of the oil in large pot or Dutch oven over medium-high heat. Add half the chicken and cook, stirring occasionally, until lightly browned but not quite cooked through about 3 minutes. Transfer the chicken to a plate. Add another 1/2 tablespoon of oil to the pot and repeat with the remaining chicken.
Add the remaining tablespoon of oil to the pot, reduce the heat to medium, then add the onion, celery, poblano and jalapeno peppers and cook, stirring occasionally, until the vegetables are softened, about 8 minutes. Add the garlic, cumin, oregano, and coriander and cook, stirring, until fragrant, about 30 seconds.
Add the beans, broth and salt and bring to a boil. Reduce the heat to medium-low and simmer, stirring occasionally, 30 minutes. Return the chicken with its juices to the pot and cook until the chicken is just cooked through, 5 minutes. Stir in the lime juice, then add hot sauce to taste, depending on the heat of the poblanos and jalapeños used, which can vary widely. Season with additional salt if desired. Top each serving with a dollop of Greek yogurt and a sprinkle of cilantro.