Rinse the chicken pieces and pat dry with paper towels.

In a bowl, combine the oil, chile powder, paprika, chipotle chiles, cumin, salt and pepper. Add the chicken pieces, turning to coat, cover, and marinate at room temperature for 2 hours or for as long as overnight. (You can store the chicken in a large zip-style plastic bag if it goes in the refrigerator.)

Prepare an indirect-heat fire in a covered charcoal grill. Place the dark meat, skin side down, on the grill rack, cover, position the top and bottom vents three-quarters open, and grill for 10 minutes. Add the breasts and wings, skin side down, re-cover, and continue grilling for 10 minutes. Turn all the chicken, re-cover, and grill on the second side until cooked through, about 20 minutes.

While the chicken grills, preheat a broiler and butter a small frame-proof baking dish. Melt the butter in a sauté pan over high heat. Add the corn and sauté until tender but not mushy, 2 to 2-1/2 minutes. Add the red pepper flakes and season with salt and pepper. Cook for a minute or two more. Remove from the heat, stir in the yogurt, sour cream, or crème frâiche, and transfer to the prepared baking dish. Sprinkle with the crumbs.

Just before the chicken is ready, run the baking dish under the broiler to brown lightly. Bring outdoors and eat grill-side with the chicken.