  We prove that the Penrose limit of a spacetime along a homogeneous geodesic
is a homogeneous plane wave spacetime and that the Penrose limit of a reductive
homogeneous spacetime along a homogeneous geodesic is a Cahen--Wallach space.
We then consider several homogenous examples to show that these results are
indeed sharp and conclude with a remark about the existence of null homogeneous
geodesics.
