  A three-dimensional effective theory for high temperature SU(3) gauge theory,
which maintains the Z(3) center symmetry of the full theory, is constructed.
Such a Z(3) invariant effective theory should be applicable to a wider
temperature range than the usual effective theory, known as EQCD, which fails
to respect the center symmetry. This center-symmetric effective theory can
reproduce domain wall and phase transition properties that are not accessible
in EQCD. After identifying a convenient class of Z(3) invariant effective
theories, we constrain the coefficients of the various terms in the Lagrangian
using leading-order matching to EQCD at high temperature, plus matching of
domain wall properties in the full theory. We sketch the expected structure of
the phase diagram of the effective theory and briefly discuss the prospects of
numerical simulations and the addition of quarks.
