In terms of its structure and intermolecular forces, why is neoprene able to stretch? I want to say it's because its carbons form a long chain which easily stretches, but I'm not sure how intermolecular forces factor into that.

After a lot of misses I found this site that explains, in very technical terms, about stretching but if you read it carefully it gets to the heart of the matter is pieces and now and then. Here is the link.
http://pslc.ws/macrog/exp/rubber/sepisode/ent.htm
The bottom line is that neoprene is a polymer that is made as a chain. If you visualize this as layers of chains; i.e. one flat chain above another flat chain above another flat chain etc, these flat chains can slide over one another easily (much like graphite layers slide over one another to give graphite very good lubricating properties. In neoprene, these flat chains are held together by S bonds; i.e., the S bridges holds the top chain to the next lower chain. This is called cross linking and the chains can be moved, say by stretching, from left to right. They aren't free to move forever because the S bridges have just so much leeway, but these crosslinkages do allow some stretching. That's about the best I can do at trying to translate that "entropy" discussion into plain language. Hope this helps. It would help if we could draw structures on this forum but that isn't possible.