If you see messages reporting file permission errors from bind named such as "could not open file '/var/named/named.pid': Permission denied", check that the path of the /run directory is correct for your system. On RHEL and Centos 7, it has moved from /var/run to /run.
Also make sure that the pid file path in named.conf matches the path in named.service, and that the pid file path is writable by the named user. If the path points to /var/named/named.pid, look at the ownership and permissions of that directory relative to the named user. It may be necessary to change the pid file path to /run/named/named.pid so that the service user is able to create the file.
Finally, ensure that the dump-file, statistics-file and memstatistics-file paths in /etc/named.conf or /var/named/chroot/etc/named.conf are writable by the named user.
Some possble locations where these paths might be set...