Pour the chicken broth into the crockpot and switch it on to low. You will never need to go to high for this recipe. (If you do, you can eat out the burnt cheese as you stand there in the kitchen. I learned this from experience!).
Add the chicken and cook until the meat is falling off the bone (at least four hours, because it's also about rendering fat, juice and flavor from the chicken itself); remove the chicken and run a fine strainer through the broth to pick up and discard cartilage or bits of skin. Refrigerate the chicken.
Add the diced tomatoes and enchilada sauce, onion, garlic and cilantro. Cook for 2 hours at minimum.
Add back the chicken meat, cut from the bone and shredded with a fork. Cook for a few hours, however long you need between tasks. At this point, you can let it cook overnight.
Taste the soup. Add coriander and cumin to taste. Add the diced Anaheim peppers and cook until the peppers are softened, at least 4 hours.
Add cheese, a bit at a time, diced as finely as possible. This part you have to watch and stir constantly - the cheese needs to become completely melted into the soup for its salt and the overall thickness and richness it will add to the soup. Continue to cook after cheese is completely integrated, about 30 minute.
Add tortilla chips and let soup cook further, until the chips disintegrate a bit. The chips will provide additional salt and will also thicken it to an almost stew-like consistency, which is the point of any crock pot soup as I see it.
After all this has been done, re-taste the soup. You shouldn't need a bit of salt, but if you do, now's the time!
Serve with shredded extra-sharp cheddar cheese (for a taste contrast) and some nice, thick sour cream. Other great toppings: fresh, chopped scallions; queso fresco; chopped onions of a color other than the one you used in the soup; crunchy tortilla chips. Slainte!