Quantitative three-dimensional (3D) chemical mapping using angle-scan spectro-tomography in a scanning transmission (soft) X-ray microscope (STXM) has been used for the first time to characterize the early stages of CaCO3 biomineral nucleation on the surface of planktonic freshwater cyanobacterial cells of the strain Synechococcus leopoliensis PCC 7942. The apparatus for STXM angle-scan tomography is described. Aspects of sample preparation, sample mounting and data acquisition and quantitative analysis and interpretation are discussed in detail. Angle-scan tomography and chemically selective 3D imaging at multiple photon energies has been combined with a complete 2D spectromicroscopic characterization of the biochemical and mineralogical composition. This has provided detailed insights into the mechanisms of mineral nucleation, leading to development of a detailed model of CaCO3 nucleation by the cyanobacterial strain S. leopoliensis PCC 7942. It shows that Ca is absorbed by the extracellular polymeric substances (EPS) of the cyanobacteria and that CaCO3 with aragonite-like short-range order is precipitated rather homogeneously within the EPS. The precipitation of the thermodynamically more stable calcite polymorph then starts at Ca-rich hot spots within the EPS and close to the cyanobacteria.