This constructs a catenary curve of arbitrary length between endpoints (volume centroids of the two end links in the chain). Length is adjusted manually so the 81 links don’t collide, but this is based only on visual inspection so avoiding collisions needs more work.
As I write this, I added a Collision Many|Many component (VERY SLOW! 29 seconds) to detect collisions and nudged the ‘Length’ slider, trying to avoid them - but apparently there is more to it than that… By the way, I just tested your existing links and they collide with each other too!
P.S. I added the purple group to determine the length of your original chain (~166 units), which got rather complicated because I had to sort the links (points) in sequence first.
P.P.S. I found a perspective that makes the link collisions more visible. Perhaps the orientation of these links is wrong because they collide regardless of the length used for the catenary curve.
This image uses length = 166 units:
