Place the ground beef in a medium pan over medium heat.
Add the chopped onion and cook until the meat is browned and the onion is soft.
Stir in the tomato paste, ketchup, chili powder, Worcestershire sauce, and vinegar.
Mix well to combine the flavors.
Reduce the heat to low, cover the pan, and let the chili simmer for about 30 minutes.
Stir occasionally to prevent sticking or burning.
Season with salt and pepper according to your taste.
Feel free to adjust the chili powder to modify the heat level.
Once the chili has thickened and flavors have melded together, remove from heat.
Serve over hot dogs in buns.