Combine stewed tomatoes, beer, hot sauce, bouillon cubes, brown sugar, chili powder, paprika, oregano, garlic powder, and cayenne pepper in a slow cooker; cook on High for 1 hour.
Heat olive oil in a skillet over medium heat; cook red onion in hot oil until tender. Stir in ground chicken; cook and stir until completely browned. Transfer mixture to the slow cooker and return the skillet to the heat. Fry sausage in the reheated skillet until completely browned and crumbly; add to the slow cooker. Mix tomato paste and kidney beans into chili. Continue cooking on High another 2 hours. Switch the heat to Low and simmer 4 hours more.