Heat a broiler to high.
Place the poblano peppers on a foil-lined baking sheet and rub with 1 ½ teaspoons oil. Broil for 10 minutes or until blackened on all sides, turning occasionally.
Wrap the peppers in foil and let stand for 10 minutes. Unwrap, remove the skins and seeds, and coarsely chop the peppers. Set aside.
Meanwhile, heat the remaining 1 ½ tablespoons oil in a large skillet over high heat. Add the onion, oregano and garlic, and sauté for 3 minutes.
Stir in the tomatoes, chile, adobo sauce and ½ teaspoon salt. Cook for 10 minutes, stirring occasionally. Stir in the peppers, lime juice and chicken. Cook 2 to 3 minutes or until slightly thickened.
Meanwhile, bring the milk to a boil in a saucepan over medium-high heat. Reduce the heat to medium-low, add the remaining ¼ teaspoon salt and the polenta. Whisking constantly, cook until thickened, about 2 minutes.
Place ¾ cup polenta in each of 4 shallow bowls. Top each serving with ¾ cup chicken mixture. Garnish with a dollop of sour cream and a sprinkle of cilantro leaves.