Even though CNAME chains are allowed in RFC 1034, you shouldn’t do that. Those chains aren’t considered to be a good practice as they impose an overhead on the infrastructure for example. Not really an issue here, but when you your own DNS infrastructure.
The client will have resolve each domain.
First domain.com which tells to go to foo. Foo tells the client to search at bar. which probably points to an IP or another CNAME. And so on.
It takes 4 attempts to resolve the target.
Currently I can’t imagine any usecase for such CNAME chains. There are probably some but …