Look up 'welders' on Yelp or any regional company directory. In cities you should find plenty of options. Be sure to describe how small the links are as some may balk at that. They'll need the right equipment to do it, something like a TIG welder that briefly gets super hot to melt a small area, then turns off before melting the link into a puddle.
You could also ask a plumber to repair it using the solder they repair metal pipes with, though I'm not sure if that would be strong enough.
It seems logical the metal is the "weak link" in the system. If you drive a frozen link over a pebble its rigidity is more likely to make it crack vs plastic which will more likely flex. The cross section of each side of the links in the chains is also much smaller than most of the plastic areas. They've made the chains small and light so they take minimal space in your trunk but I think that makes it inevitable one will break eventually due to bad luck with road debris if you use the chains often enough.
The smallest link listed there is 13/64" (0.2") which I think refers to the diameter of the metal making the link. Trak's chains are 3.00 to 3.20mm (~0.12") diameter as measured with callipers.