Heat a large saucepan or Dutch oven over medium-high heat. Add the ground beef and cook for 5-8 minutes, stirring occasionally. When the beef is browned, remove it from the pan.
Add the olive oil and diced onion. Cook, stirring occasionally, for 5 minutes or until the onion is tender.
Next, add the garlic and tomato paste and cook for one minute.
Add the ground beef back to the pan along with the tomato sauce, water, beans, chili powder, Worcestershire sauce, and oregano.
Bring the mixture to a boil and then reduce it to a simmer and cook for 15 minutes, stirring occasionally.
Remove the chili from the heat and set it aside while you prepare the hot dogs.