Put the chicken breasts in a gallon plastic bag and pour the lime juice over them. Seal the bag and allow to marinate about 20 to 30 minutes.
Turn the oven on to broil and preheat the grill while the chicken marinates. Grill should go to medium/medium-high heat, about 400° F/200° C.
Place the halved tomatillos on the baking sheet and broil in the oven until the tops are charred, about 5 to 10 minutes. Puree the tomatillos plus their juices in the blender.
Rub the grill with oil and place the drained chicken breasts, onions, bell peppers, and Anaheim peppers on the grill. Grill the chicken, about 7 to 8 minutes per side. Turn the onions and peppers as each side blackens and blisters, about 4 minutes per side.
Remove the chicken and shred with a fork. Dice the onions, and seed and chop the peppers.
Warm the pot over medium-high heat and add the oil, then the cumin, chili powder, and black pepper. Sauté until the spices release their aroma, then add the onions and peppers. Cook, stirring, about 1 to 23 minutes, then pour in the tomatillo puree and chicken broth. Stir until everything is well combined, then add the shredded chicken. Bring to a boil, then simmer partly covered for about 20 minutes. Taste and add salt to taste.