Cook the chorizo in a small nonstick skillet over medium heat, stirring occasionally, until crisp, about 5 minutes. Transfer to a bowl using a slotted spoon; set aside. Reserve the drippings; let cool slightly.
Combine the chile, scallions, cilantro, garlic, oregano and cumin in a food processor. Add 2 tablespoons water, the reserved drippings, the lime juice and 1/4 teaspoon salt; pulse to make a coarse paste. Transfer the paste to a large bowl, add the chicken and toss to coat; cover and refrigerate at least 30 minutes or up to 4 hours.
Preheat the oven to 425 degrees F. Tear off four 16-inch sheets of parchment paper. Make the packets (see photo gallery): Arrange 3 slices polenta on one sheet of parchment; top with one-quarter each of the bell peppers, chorizo and chicken. Seal as directed. Repeat to make 3 more packets; divide between 2 baking sheets.
Transfer to the oven and bake until the parchment puffs and the chicken is cooked through, about 30 minutes. Let rest 5 minutes. Carefully open the packets; sprinkle with the cheese and serve with lime wedges.