Cut Anaheim, and poblano chiles in half, remove the seeds , char and peel.
In a large skillet, heat the olive oil and saute the onion until translucent. Add the garlic, jalapeno chiles, cumin and oregano, and saute for several minutes. Add the chicken stock and bring to a simmer.
Then add the potatoes and cook until just tender. With a slotted spoon, remove 1 cup of potatoes and reserve. Add the diced chicken and poach gently in the onion/chili/potato mixture until chicken is cooked through.
Remove from the heat immediatly, transfer to a bowl, reserving 1/2 cup of the liquid in a small bowl. Refrigerate the remainder to keep the chicken from overcooking.
In a blender, puree the reserved potatoes, half the Anaheim and half the poblano chilies, and the cilantro with the reserved half cup of liquid. When the chicken mixture is no longer warm, add the puree.
Dice the remaining half of the Anaheim and poblano chilies in 1/2" cubes and add to the mixture. Season with salt. Reheat just before serving to retain the fresh green color and flavor of the soup.