In a very large (6-quart) Dutch oven, heat the oil over medium-high. Add about two thirds of the onion and cook, stirring regularly, until richly browned.
Add the salsa and broth and bring to a boil. When the sauce is at a rolling boil, turn off the heat and stir in the chips and shredded cheese. Press the chips down to ensure that nearly all are submerged; a few on the top may still be sticking out.
Strew the chicken over the top, cover and let stand for 3 or 4 minutes. Gently stir everything together, then drizzle with the crema, and sprinkle with the onion, optional grated queso anejo and cilantro. Serve without hesitation.