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.