Periodic antidot arrays imposed upon two-dimensional hole systems (2DHSs) display a striking dependence of the positive low-field magnetoresistance on the in-plane crystallographic orientation of the superlattice. An enhanced positive magnetoresistance can be ascribed to the 2DHSs non-circular Fermi surface which stabilizes chaotic trajectories for specific crystallographic directions. The erect provides a first example of the role of non-spherical Fermi surfaces on the classical chaotic dynamics of charge carriers. Transport calculations taking into account both the classical chaotic motion of the holes in antidot lattices and the warped Fermi contour confirm this picture.