The heat capacity of bundles of closed-cap single-walled carbon nanotubes with one-dimensional chains of nitrogen molecules adsorbed in the grooves has been first experimentally studied at temperatures from 2 K to 40 K using an adiabatic calorimeter. The contribution of nitrogen C N2 to the total heat capacity has been separated. In the region 2 8 К the behavior of the curve C N2 (T) is qualitatively similar to the theoretical prediction of the phonon heat capacity of 1D chains of Kr atoms localized in the grooves of SWNT bundles. Below 3 К the dependence C N2 (Т) is linear. Above 8 К the dependence C N2 (Т) becomes steeper in comparison with the case of Kr atoms. This behavior of the heat capacity C N2 (Т) is due to the contribution of the rotational degrees of freedom of the N 2 molecules.