Many years ago I saw a Japanese TV program that explored the food of southern Taiwan and one of the stops was a restaurant that had a 106-year old vat of broth. It was tall and narrow and had a giant hump of crust on one side.
If it's still open, it would be going for 130+ years at this point.
ETA: Found it. Established 1895, the year Taiwan was annexed by Japan. It's not soup, it's a meat sauce (滷肉) used on a noodle dish. Scroll down to the middle of the page, which shows the chef with the pot in front of him.
Cool. The pot is surprisingly small. Is the sauce in it highly concentrated or something?