I have developed a technique to solve for the khronon field in a space-time containing a slowly moving black hole in the khrono-metric regime of Hořava Gravity. To develop these solutions I first revisited the khronon field around static spherically symmetric black holes and perturbed them by a small velocity. The equations of motions of the perturbed field were identified along with the linearly dependent series expansions at the boundary points. Using the boundary conditions and equations of motion the khronon field was numerically solved throughout the space-time. These solutions were used to calculate a sensitivity parameter which defines how the black hole mass appears to be modified due to its velocity. It was found that the sensitivity parameters are highly suppressed and black holes should appear similar to their general relativity counterpart. / Thesis / Master of Science (MSc) / I have investigated slowly moving black holes in a theory of modified gravity. The goal was to see whether the theory breaks down in modelling these black holes and if not, is it possible to test the theory using these predictions. I ultimately found that this theory can model the slowly moving black holes and would appear almost indistinguishable from classically moving black holes. This means that slowly moving black holes on their own will not provide a sufficient test of the theory.