  We show that the gravitational phase space for the near-horizon region of a
bifurcate, axisymmetric Killing horizon in any dimension admits a 2D conformal
symmetry algebra with central charges proportional to the area. This extends
the construction of [Haco et. al., JHEP 12, 098 (2018)] to generic Killing
horizons appearing in solutions of Einstein's equations, and motivates a
holographic description in terms of a 2D conformal field theory. The Cardy
entropy in such a field theory agrees with the Bekenstein-Hawking entropy of
the horizon, suggesting a microscopic interpretation.
