Position an oven rack 5-6 inches from the broiler element and heat the broiler to high. Line the bottom of a broiler pan with foil and replace the perforated top part of the pan.
Broil the poblanos, turning 3 times, until blackened, 12-15 minutes total. Put the poblanos in a medium bowl, top with a dinner plate, and let stand for 5 minutes. Set aside broiler pan for cooking chicken.
Meanwhile, cut the lime in half. Cut one half into wedges and squeeze the other half to get 2 teaspoons juice. Measure the juice into a small bowl and stir in the sour cream or crema and the chopped cilantro.
Transfer the poblanos to a cutting board to cool a bit, then peel away the burned skin, discard the stems and seeds, and cut into 1/2-inch dice. Add to the sour cream mixture and stir to combine. Season to taste with salt.
In a small bowl, combine the 2 teaspoons salt with the coriander, cumin, and pepper. Coat the chicken with the oil and season on both sides with the spice mixture.
Put the chicken skin-side down on the broiler pan, and broil until well browned, 7-10 minutes. Turn the chicken over with tongs and continue to broil, checking frequently, until the chicken is dark brown and cooked through (an instant-read thermometer should register at least 165 degrees F), 4 to 6 minutes more. If the chicken threatens to burn before it's cooked through, move the pan to a lower rack.
Transfer the chicken to serving plates, spoon the poblano sour cream on the side, and garnish with cilantro sprigs, if using, and the lime wedges for squeezing over the chicken. Serve hot.
HINT: If you want to "kick it up a notch," considering brining chicken in a salted lime water bath for no more than an hour before cooking. Use about 1/4-cup salt to 4 cups cold water to 1/2-cup lime juice. YUM! Make sure to rinse well and pat dry before cooking.