Boot off of the installation cd using "linux rescue"
Unmount all of the drives in /mnt/syslinux
Note: Before unmounting /mnt/syslinux itself, you must unmount all of the mountpoints within it.
$ resize2fs /dev/VolGroup00/ 5G
... boot back into regular linux ...
$ lvreduce -L 6GB /dev/VolGroup00 (answer yes)
$ lvcreate -L 10G -n var VolGroup00
... boot back into rescue mode ...
mkfs -t ext3 /dev/VolGroup00/var
mount -t ext3 /dev/VolGroup00/var/ /mnt/var
mv /mnt/syslinux/var* /mnt/var
(edit fstab so that it mounts the new logical volume to /var)
resize2fs /dev/VolGroup00/LogVol00 (remember how I made this 5Gb when the LV was 6GB?)
On rebooting, syslogd had a problem starting. (Running in debug mode, it would complain of "permission denied" to /var/log/secure and all other log files). It was an SELinux problem and was remedied by relabeling the filesystem.