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 to 40 K using an adiabatic calorimeter. The contribution of nitrogen <$EC sub roman N2> to the total heat capacity has been separated. In the region 28 K the behavior of the curve <$EC sub roman 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 K the dependence <$EC sub roman N2 (T)> is linear. Above 8 K the dependence <$EC sub roman N2 (T)> becomes steeper in comparison with the case of Kr atoms. This behavior of the heat capacity <$EC sub roman N2 (T)> is due to the contribution of the rotational degrees of freedom of the N2 molecules.

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