Heat the oil in a medium saucepan over medium heat. Add the garlic, hominy, chili powder, jalapeño, and cumin. Cook for 3 minutes, stirring frequently.
Add the cilantro, onion, tomato puree, and chicken stock. Bring to a boil, reduce the heat slightly, and simmer, uncovered, for 20 minutes.
After soup has simmered, add cheese, lime juice, salt and pepper. Add soup to a blender and blend until smooth. If the soup is too thick, thin with a little bit of chicken stock.
Divide soup between four bowls, top tortilla chips, and serve.