Roast the poblano over an open flame turning regularly for about 5 minutes, or until blackened all over. This can also be done under the broiler for 10 minutes. Make sure the chile is about 4 inches from the flame. Cover the poblano chile with a towel once rit has finished roasting.
Heat the oil in a medium saucepan over medium heat. Saute the onion and garlic about 8 minutes, or until onion starts to look translucent. Press the onion and garlic against the side of the pan with a slotted spoon trying to leave a fair amount of oil in the pan. Set the pan aside for later use.
Transfer the garlic and onion to a food processor or blender. Add the corn, cornstarch and 1 1/2 cups milk. Puree.
Strain the soup through a medium mesh strainer into the saucepan. Heat over medium and whisk often as the soup comes to a simmer.
Once the chile is cool enough to handle, rub off the blackened skin. Pull out the stem and seeds. Rinse to remove any remaining bits. Cut into a 1/4 inch dice and stir into soup along with the chicken and remaining milk.
Simmer until the chicken is cooked through, about 10 minutes. Season with salt to taste and serve garnished with cilantro.