This issue is fairly well documented, but I wanted to put it here for my own purposes:
When installing a new ADFS farm, you may find that if you reboot the ADFS server, or restart the ADFS service, it will not restart and fails with a 1297 error code. In the Event Viewer you will see an error stating that;
A privilege that the service requires to function properly does not exist in the service account configuration
This error screams of an issue with the configuration of the service account…and that’s exactly what it is. On the affected ADFS server, open the Local Security Policy console (secpol.msc) and expand the following container:
Security Settings\Local Policies\User Rights Assignment
Go into the properties of the Generate Security Audits section and add the ADFS service account into here. If the option to add an account is grayed out, then that means that a Group Policy is controlling this access list, and you will need to find and modify the appropriate GP to add the ADFS service account into the group (usually the Default Domain Policy). While you are here, ensure that the ADFS service account has ‘Log on as a Service’ privileges.
Once this is done you should be able to start the ADFS service (although if you edited Group Policy then run gpudpdate first). Hopefully this helps you before you get to the point where you make the ADFS service account a Domain Admin! Remember, this account only needs Domain User privileges and should not be put into god mode!