Other designs for connecting chain links that I saw seemed like the connector would be the weak link in the chain. So I designed an extra strong connector that should be nearly as strong as a regular chain link of the same size. 

I have tested it "very scientifically :-)" and found that it can hold at least 10kg with no sign of stress. My test was printed PLA with only 3 perimeters and no infill. PLA will bend and become brittle with time so it isn't the ideal material. But printing this in some other material like carbon fiber or even better, super materials should make a usable chain. 

If anyone does some actual tests, I'd be interested in the results.

You can use the slender version of this chain with my shackles and manacles design if you wanted a better chain: