There are many sets like that but fortunately, you can search for plastic chess set and find thousands of images to help you narrow down your search.
The thing that rattled was probably a weight.
Vintage chess set
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Moved to Chess Books & Equipment, you might get more replies here.
Start with google images for Drueke, Cavalier, or Gallant Knight. If you don’t see it there, try Duncan Pohl’s book below. Since it was made 70s and earlier, is plastic, and you are in the U.S., seems a good chance it was distributed by a U.S. company.
https://www.scribd.com/document/62620988/USA-Chess-Sets
Thanks so much for the responses. Definitely gives me somewhere to start!
Here's a possibility. E.S. Lowe company's Renaissance chessmen. Very popular in the 60s and 70s. The piece with something rattling around inside could have had a loose weight. My set did that. Hope this helps. Good luck!
@kimmoyers - good luck with the search, I am sure it will bring back fond memories if you find it. Here’s a plastic set that I have - was it like that perhaps? If so, following Chess Author ‘s advice might help you find an US-made version of the set. 
I really like this set - plastic as it may be - I thinks it’s wonderful. 👍
I have a chess set form the 1980s when my grandfather visited the ussr
Just in case I want to add something. Don’t dismiss the pieces as necessarily inferior just because they may be made from plastic. The quality of plastic varies very widely. There is high quality durable plastic that is very pleasant to touch and there is cheap plastic which can chip and break quickly.
Some old “plastic” pieces were made from high quality materials similar to melamine and similar to celluloid. Some of them are still very valuable and rare to find.
Some old “plastic” pieces were made from high quality materials similar to melamine and similar to celluloid. Some of them are still very valuable and rare to find.
Hello-
New to this site. I have an impossible question most likely, but hoping someone out there might recognize something I say about a chess set I’m looking to find. My Dad taught me back in the 70’s to play. I’m sure his set was older than that. I can’t find the set anywhere. So I’m on a quest to find a similiar one.
I remember it was in a pretty good size (maybe 20” x 18”) whitish-colored box. It was made out of a heavy weight cardboard. It seems like it had some writing in the very center of the lid. The board was in the center of the box folded in half. It had a light blue backing. The black and white chess pieces were separated by color and stored on either side of the board in the box. The pieces were made of some kind of plastic-like or resin material. They were pretty good size pieces with the king being somewhere around 4-5” tall. I can’t really remember exactly what the pieces looked like. It seems like they looked more life like than abstract. I remember holding one of the pieces in my hand, maybe the bishop, and it had something loose inside of it that felt like a ball inside that moved around. It was the only piece like that. It was as if something formed inside of it out of the plastic material over the years. But you couldn’t tell anything was wrong with it from the outside.
I’m not looking for anything about value. I would just like to find a set similiar. My Dad recently passed away.
I’m now 50 years old. I can’t figure out where we would have stored the set or what could’ve possibly happened to it.
Like I said originally, this is probably an impossible feat, but if any of these details ring a bell for anyone out there, I’d appreciate anything you may know about this set. Or, if anyone knows of a place or website I can go to in order to see pictures of older sets that would be great! Thanks so much for taking time to read my post and any help anyone can offer!