  I introduce the notion of a parity horizon, and show that many simple
solutions of shape dynamics possess them. I show that the event horizons of the
known asymptotically flat black hole solutions of shape dynamics are parity
horizons and that this notion of parity implies that these horizons possess a
notion of CPT invariance that can in some cases be extended to the solution as
a whole. I present three new solutions of shape dynamics with parity horizons
and find that not only event horizons become parity horizons in shape dynamics,
but observer-dependent horizons and Cauchy horizons do as well. The fact that
Cauchy horizons become (singular) parity horizons suggests a general chronology
protection mechanism in shape dynamics that prevents the formation of closed
time-like curves.
