The chain.pem contains only the intermediate certificate, so if they require a file that contains only the intermediate certificate, that file should work.
The fullchain.pem contains both the end-entity certificate (your certificate) and the intermediate certificate in one file, so if they require a file that contains both together, that file should work.
Given that you have the private key in privkey.pem, there’s no other information that should be necessary for a hosting provider.