Tear the chile in half lengthwise and remove the seed pod and seeds. Toast it in a hot dry pan over medium heat, pressing it flat for a few seconds, then flipping it over and pressing it again. Break the chile into pieces and put in a blender jar along with the tomatoes with their juice. (A food processor will work, though it won’t completely puree the chile.)
Heat the oil in a medium (3- to 4-quart) saucepan over medium-high. Add the onion and garlic and cook, stirring frequently, until golden, about 7 minutes. Scoop up the onion and garlic with a slotted spoon, pressing them against the side of the pan to leave behind as much oil as possible, and transfer to the blender. Process until smooth.
Raise the heat under the pan to medium-high. When quite hot, add the puree and stir nearly constantly, until thickened to the consistency of tomato paste, about 6 minutes. Add the broth and epazote. Reduce the heat to medium-low and simmer for 15 minutes. Taste and season with salt, usually about a generous teaspoon (depending on the saltiness of the broth).
Just before serving, add the chicken to the simmering broth. Divide the avocado, cheese and tortilla chips between serving bowls. When the chicken is done, usually about 5 minutes, ladle the soup into the bowls.