Uh, yes it had many links. Excellent deduction, Watson! I'm sure you can fathom that not all of them exist anymore. Even the ones on display at West Point are not original, but rather are reproductions because they don't have the original links at their disposal. They're not something we can find on eBay.
I don't doubt the hardiness of the links. My thought was that someday there will be the awkward conversation that starts with "We put it in the river RIGHT HERE, I swear it! It has to be around here somewhere, sir..."