In a large heavy bottomed pot heat olive oil over medium heat. Add onion and sauté until translucent, about 3 minutes.
Add potatoes, broth and water to pot, and bring to a boil. Lower heat to simmer and partially cover pot. Simmer until potatoes are tender when pierced with a knife, about 20 minutes.
Meanwhile char Hatch or poblano chiles under a broiler or on a grill until blackened on all sides. Place chiles in a zip lock or small paper sack to steam until cool, peel charred skin and coarsely chop.
When potato is tender, transfer to a food processor with chiles, corn, and cilantro. Puree until almost smooth, then slowly add cooking stock and puree. Soup should still be chunky.
Return soup to saucepan and bring to a low simmer, add cooked chicken and heavy cream, and season to taste with cumin, salt and pepper. Serve with lime wedges. green tabasco sauce, and additional cilantro if desired.
Store in airtight container in refrigerator for 3-4 days.