Blacken the skin of the pobanos by sitting them over the burner on your stove. Turn regularly until evenly blackened, about 5 minutes total.
Transfer to a plastic bag to steam for 15 minutes.
Pour the oil into a large skillet set over medium-high heat. Season the chicken breasts with salt, and then place in the skillet. Cook until well browned, about 2 minutes a side. Set aside.
Meanwhile, blend the tomatillos and cilantro.
Pour this into the skillet when the onions are done. Cook until it is very thick, about 8 minutes.
Add the broth, poblano strips, and the crema. Stir well, and season with a teaspoon of salt. Return the chicken breasts to the skillet. Reduce the heat to a simmer and cook until the chicken is completely cooked, about 8 to 10 minutes.