A non-covalent approach to debundle single wall carbon nanotubes using a biocompatible chitosan-derivative, namely N-octyl-O-sulfate chitosan (NOSC), was investigated. The resulting stable dispersions were characterised by Raman spectroscopy, UV-Vis spectroscopy, atomic force microscopy (AFM), transmission electron microscopy (TEM) and zeta-potential measurements. Both AFM and TEM studies revealed the presence of individual carbon nanotubes wrapped with the polymer (diameters up to 7 nm). Raman spectra showed radial breathing mode frequency shifts, after the addition of NOSC, due to the wrapping of the biomolecules onto the graphitic sidewalls. Molecular modelling studies were employed to investigate the mode of binding of the NOSC chains to the surface of the nanotubes. In agreement with the experiments, modelling studies predicted that the wrapped tube has a maximum thickness of approximately 7 nm. Studies on the anticoagulant properties of these complexes revealed that NOSC coated SWCNTs exhibit similar activity to the polymer alone, this property would eliminate the risk for SWCNTs to induce coagulation as a host reaction process when used in vivo.