In a Dutch oven or large stock pot, heat the oil over medium-high heat.
Once hot, add the onion, celery, carrot, chipotle chile, cumin, chili powder, and garlic. Cook for 6 to 8 minutes, stirring occasionally, until the carrot is cooked through but still crisp.
Add the stock, hominy, and tomatoes, then bring everything to a boil. Reduce the heat, cover, and simmer for about 10 minutes, stirring occasionally.
Add the shrimp and cook until they just turn opaque, about 2 minutes.
Remove from heat and stir in lime juice and salt. Garnish with crumbled tortilla chips, avocado, and cilantro.