  We present a general class of natural theories in which the Higgs is a
pseudo-goldstone boson in an orbifolded gauge theory. The symmetry protecting
the Higgs at low energies is an accidental global symmetry of the quadratic
action, rather than a full continuous symmetry. The lightest degrees of freedom
protecting the weak scale carry no Standard Model (SM) quantum numbers and
interact with visible matter principally through the Higgs portal. We find that
the twin Higgs is the simplest example of an orbifold Higgs. This opens the
door to the systematic study of "neutral naturalness": natural theories with
SM-neutral states that are as yet untested by the LHC.
