It is my considered impression that chain doesn't "stretch", except under extreme load.
Elongation is due to wear, though it could happen due to exceeding the elastic limit. Chains are not guitar strings, so don't "tension" them. If a chain wears and elongates more than a couple of percent, then you'll have problems with tooth spacing and are in a world of hurt.
Have a look around here:
http://chain-guide.com/toc.html