Cook beef and onion in a large Dutch oven over medium heat until beef is browned and crumbly; drain and return to pot. Add tomato paste; cook, stirring, 2 minutes. Add tomato sauce, diced tomatoes, broth, and seasoning mixes; bring to a boil, reduce heat, and simmer 20 minutes.
Divide chips among bowls. Top with chili, lettuce, cheese, and sour cream.