[Signalman]

The Constitution does NOT require any background checks for presidential eligibility

That is correct. But in order to have access to classified information, especially Sensitive Compartmented Information (SCI), a full Background investigation is required. Is this waived for the President? I honestly don't know.

And what about classified information designated as "NOFORN" (Not releasable to Foreign Nationals).

So could someone serve in the office of POTUS and not be allowed access to classified information? And could certain agencies of the US government unilaterally deny certain information to the POTUS because they (the agency) deems him to be untrustworthy?

Just throwing these questions out there.

[Peerless]

That is correct. But in order to have access to classified information, especially Sensitive Compartmented Information (SCI), a full Background investigation is required. Is this waived for the President? I honestly don't know.

There are only three qualifications to hold the office of President. Thirty-five years of age, natural born citizen, fourteen years a resident of the US.

That's it.

Oh, and of course you first have to have received the requisite number of electoral votes. ;)

But to add anything else, you'd need to amend the Constitution.

[Reily]

The Constitution grants access by virtue of office.
Look at Ron Dellums! He was an avowed unapologetic Communist and not only served but I believe was Chair of the House Select Committee on Intelligence.