In a large saucepan, heat oil over medium. Cook garlic and chili powder until fragrant, about 1 minute. Add tomatoes (with juice), beans, broth, corn, and 1 cup water; season with salt and pepper.
Bring soup to a boil; reduce to a simmer. Add tortilla chips; cook until softened, about 2 minutes. Remove from heat; stir in lime juice, and season with salt and pepper. Serve soup with lime wedges and, if desired, more chips.