What is the highest non-elected, non-appointed position in the US government today?

FLOTUS?

pinkfreud-ga may be right. The First Lady of the United States
(FLOTUS) sounds like a pretty fair guess. Everybody else is either
elected or appointed. Are the Joint Chiefs of Staff appointed? I know
the chairman is. Maybe there's an angle.

If they aren't elected, and they aren't appointed, what are they?
Earned? Like moving up in a company? I don't know. Even the White
House chef is appointed by the FLOTUS. Hard to say; especially for $2
I imagine.

In order to answer this question one must first define "non-appointed position." 

If by non-appointed, one means not commissioned or appointed by the
congress or executive branch, than I suppose a federal employee, such
as a SES level-4(senior executive service, civilian equivalent to a
military general) would be the answer, unless being "selected" for a
position by an agency counts as being appointed.

More importantly, you must define "highest". Does this mean authority,
power, position, prestige or what?