What you want is Mandatory Access Control. It allows you to specify a set of permissions which the kernel will not allow to be overridden, even by root. SELinux is one well-known such system, Smack is another example, and AppArmor is a third such system. In Linux, they are implemented as Linux Security Modules, a general-purpose facility for controlling access outside the traditional UNIX-like security model. In addition to the existing general-purpose systems, you could of course create your own for a special purpose.
Of course, root has the ability to turn the entire facility on or off or change the MAC permissions of files, and some of these systems even allow those capabilities to be granted to non-root users. However, it's also possible, depending on the system, to disable this ability. I know SELinux and Smack make this possible; I doubt all LSMs do. Once disabled, the only way to regain the ability is to reboot the kernel. You will then want your boot process to disable the capability before user access is enabled. If your kernel and boot process are secure, such a configuration could (at least in theory) be changed only by physically removing the storage media to change it.
As an example, if you were using SMACK, you could do:
chsmack -a _ <file>
This would set the file to have the special label "_" which allows only read or execute access, but never write. Now even root cannot write this file (once SMACK has been activated and the security override capability has been disabled, as mentioned above).
However, you must also ensure that your kernel is secure. By default, it is easy for root to subvert the kernel, because the kernel trusts the root user. If root can just remove the security module, it doesn't help very much. A list of such methods is here, but note that no such list can ever truly be complete for all circumstances.
Finally, depending on your circumstances, you may need to secure your boot process. For a machine where you have sole physical access, this might not be needed, but for maximum security you really want encrypted filesystems and a secure way of booting the kernel, such as UEFI Secure Boot.