  Recently Harada has proposed a gravitational theory which is of third order
in the derivatives of the metric tensor. This has attracted some attention
particularly as it predicts a late-time transition from cosmological
decelaration to accelerated expansion without assuming the presence of dark
energy or a non-zero cosmological constant. This theory has been dubbed
conformal Killing gravity by Mantica & Molinari.
  The most general exact solutions of the Harada field equations are known for
a number of important physical situations: homogeneous and isotropic
cosmological models, static spherically symmetric vacuum and electrovac
spacetimes. These are analogues of the well-known FRWL, Schwarzschild and
Reissner-Nordstr\"om metrics of General Relativity(GR). In this study the
pp-waves in Harada's theory are studied and the most general exact solution is
obtained together with its specialisation for plane waves. The generalisation
from GR to Harada's theory turns out to be straightforward and the solutions
only involve an extra non-propagating term. The solutions have Petrov type N
(or 0) and the Ricci tensor is either zero or the Segr\'e type is [(211)] with
zero eigenvalue.
  For any metric in conformal Killing gravity it is shown that more than one
possible matter source can generate the solution. If the metric admits one or
more Killing vectors, the ambiguity in the possible matter sources increases.
