In simple magnetic materials (e.g. ferromagnets, antiferromagnets, etc) electronic spin is typically aligned either parallel or antiparallel to a single axis, and such so-called collinear systems have long been amenable to calculations within planewave implementations of density functional theory. In more complex magnetic materials, the possibility of non-collinear spin arises, where phenomena such as spin spirals and helices may occur. What is less often considered, however, is that these apparently exotic states can also be found in apparently simple materials when the symmetry is lowered, for instance at the surface of the material. A modest number of relevant surface calculations have been reported in the literature, but until recently the vital description of spin-orbit coupling has been included in very few popular density functional codes; the recent implementation of this feature in the CASTEP computer code is a major step forward in this respect. This project aims to investigate non-collinear spin specifically at chiral surfaces - these are surfaces created or modified such that they possess no improper symmetry elements (mirror or glide symmetry). Chiral surfaces have long been of interest for their potential in conducting asymmetric catalysis (preferentially catalysing the production of either left- or right-handed versions of organic molecules) but their physical properties have been largely overlooked. There exist exciting possible applications of chiral surface magnetic phenomena in the areas of chiral sensing (using magnetism to quantify surface chirality) and chiral control (using magnetism to direct chemical asymetry). The aim here is to achieve the fundamental understanding necessary to enable such applications.