Using a new micro-SQUID setup, we investigate magnetic anisotropy in a single 1000-atom cobalt cluster. This system opens new fields in the characterization and understanding of the origin of magnetic anisotropy in such nanoparticles. For this purpose, we report three-dimensional switching field measurements performed on a 3 nm cobalt cluster embedded in a niobium matrix. We are able to separate the different magnetic anisotropy contributions and evidence the dominating role of the cluster surface.