Start by charring the polbano on an open flame or under the broiler. Turn until all sides are charred. Zip up in a plastic bag so the poblano can steam. This makes the charred skin easy to peel off. Peel skin off, remove seeds and stem and dice up.
As the poblano chars, start the filling. Heat 1 tbsp olive oil in an oven-proof saute pan over medium heat. Add onion, garlic, green chili powder, oregano, cumin, salt and pepper. Cook for 7 minutes, until onions are soft. Add corn, poblano, and an additional dash of salt and pepper. Saute for 3 minutes. Turn off heat. Transfer to a mixing bowl and stir in cheese and Greek yogurt. Taste and adjust seasoning.
Butterfly chicken breasts. Press your hand on the top of the breast and with the tip of a sharp knife begin to cut into the middle of the breast. Try to keep both sides even and continue to slice the chicken in two even halves. Don't cut all the way through. Salt and pepper both sides of the chicken.
Stuff each chicken breast with the corn mixture. Close the breast with toothpicks. It's messy, but you'll figure it out.
To the same saute pan, add another tbsp of olive oil. Crank the heat up to medium-high. Drop in the chicken breasts and let cook on one side for 4 minutes. Turn over and pop the pan into the oven. Let cook in oven for 10-12 minutes.