Tholins are complex C,N-containing organic compounds produced in the laboratory. They are considered to provide materials that are analogous to those responsible for the haze observed in Titan's atmosphere. These compounds present an astrobiological interest due to their ability to release amino acids upon hydrolysis. Their chemical structure has been investigated using a large number of techniques. However, to date no detailed nuclear magnetic resonance (NMR) study has been performed on these materials despite the high potential of this technique for investigating the environment of given nuclei. Here 13C and 15N solid state NMR spectroscopy was applied to obtain new insights into the chemical structure of tholins produced through plasma discharge in gaseous N2-CH4 mixtures designed to simulate the atmosphere of Titan. Due to the low natural abundance of these isotopes, a 13C and 15N-enriched tholin sample was synthesized using isotopically enriched gas precursors. Various pulse sequences including 13C and 15N single pulse, 1H-13C and 1H-15N cross polarisation and 1H-15N-13C double cross polarisation were used. These techniques allowed complete characterisation of the chemical and structural environments of the carbon and nitrogen atoms. The NMR assignments were supplemented and confirmed by ab initio electronic structure calculations for model structures and molecular fragments.