Postfix TLS certificates not found

I replaced the default snakeoil certificate for Postfix with my own cert and key. The following configuration in /etc/postfix/main.cf works:

smtpd_tls_cert_file=/etc/ssl/certs/public.cer
smtpd_tls_key_file=/etc/ssl/private/private.key

But when I concatenate the key and cert into a single file and use the recommended syntax for Postfix 3.4

smtpd_chains_files = /etc/postfix/chains.pem

smtpd warns about missing certificates (postfix/smtpd: warning: No server certs available). chains.pem is present in /etc/postfix, and is readable by root. What could be the problem here?

Thanks, Jan