  We search for solutions describing slowly moving black holes in the
khrono-metric model, a modified gravity theory with preferred time (khronon)
which arises at low energies from the non-projectable Horava gravity. We work
in the decoupling limit when the back-reaction of the khronon on the metric is
small and can be treated perturbatively. For a given black hole velocity, we
find a family of solutions parameterized by the khronon propagation speed and
regular everywhere outside the universal horizon. On the universal horizon they
have a weak singularity manifesting itself in a non-analyticity of the khronon
field. Using the behavior of khronon at infinity we extract the leading black
hole sensitivity for which we obtain a simple analytic expression valid
throughout the phenomenologically allowed parameter space.
