Heat the broiler to high. Place the poblanos under hot broiler and char until blackened an all sides, 10 to 12 minutes. Leave the door of the oven cracked to allow the steam to escape. Place the peppers in a bowl and cover tightly with plastic wrap. Allow the peppers to cool enough to handle.
While peppers char, heat extra-virgin olive oil in a high sided skillet over medium-high heat. Add chicken and lightly brown, 3 to 4 minutes. Stir in onions, jalapeno and garlic and cook to soften onions about 5 minutes. While onions cook, place tomatillos and cilantro in the food processor and process until smooth. Pour the tomatillos into the chicken mixture and stir to combine. Stir in chicken stock and honey, season with salt and pepper and simmer chili 10 minutes.
When poblano peppers are cool enough to handle, remove seeds and chop, stir into chili. Remove chili pan from heat and stir in lime juice. Add dollops of creme fraiche on top of the chili, placing spoonfuls evenly across the pan. Cover the pan with a layer of crushed chips and top with Swiss and Monterey Jack cheeses. Place under broiler until brown and bubbly. Serve from hot skillet, spooning out chili into shallow dinner bowls. TOUCHDOWN!
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