[en] Surface atomic-layer (SAL) superconductors consisting of epitaxially grown metal adatoms on a clean semiconductor surface have been recently established. Compared to conventional metal thin films, they have two important features: (i) space-inversion symmetry-breaking throughout the system and (ii) high sensitivity to surface adsorption of foreign species. These potentially lead to manifestation of the Rashba effect and a Zeeman field exerted by adsorbed magnetic organic molecules. After introduction of the archetypical SAL superconductor Si(111)-(√7 × √3)-In, we describe how these features are utilized to engineer a topological superconductor with Majorana fermions and discuss its promises and expected challenges. (paper)