Roast the poblanos over an open flame or close up under a preheated broiler, turning until blistered and blackened all over. Let cool until handleable, then rub off the blackened skin, tear open and pull out the seed pod. Rinse the poblano briefly to get rid of stray bits of blackened skin and seeds. Cut into ¼-inch strips that are about 2 inches long.
In a large (10-inch) skillet over medium-high, heat the oil. When hot, add the onion and cook, stirring regularly until lightly browned, 4 or 5 minutes, then add the garlic and stir continually for about 45 seconds, until fragrant. Finally stir in the poblano strips, oregano, crema and kale. Keep cooking (it may be helpful to reduce the temperature to medium here) until the kale is tender and the crema has reduced enough to coat everything richly. Stir in the chicken, cook for a couple of minutes to heat it through, then serve with warm tortillas for making tacos.