Context. An accurate analysis of the physical-chemical conditions in the regions of the interstellar medium in which C 3 is observed requires knowing the collisional rate coefficients of this molecule with He, H 2 , electrons, and H. Aims. The main goals of this study are to present the first potential energy surface for the C 3 +H 2 complex, to study the dynamics of the system, and to report a set of rate coefficients at low temperature for the lower rotational states of C 3 with para-and ortho-H 2 . Methods. A large grid of ab initio energies was computed at the explicitly correlated coupled-cluster with single-, double-, and perturbative triple-excitation level of theory, together with the augmented correlation-consistent quadruple zeta basis set (CCSD(T)-F12a/aug-cc-pVQZ). This grid of energies was fit to an analytical function. The potential energy surface was employed in closecoupling calculations at low collisional energies. Results. We present a high-level four-dimensional potential energy surface (PES) for studying the collision of C 3 with H 2 . The global minimum of the surface is found in the linear HH-CCC configuration. Rotational deexcitation state-to-state cross sections of C 3 by collision with para-and ortho-H 2 are computed. Furthermore, a reduced two-dimensional surface is developed by averaging the surface over the orientation of H 2 . The cross sections for the collision with para-H 2 using this approximation and those from the four-dimensional PES agree excellently. Finally, a set of rotational rate coefficients for the collision of C 3 with para-and ortho-H 2 at low temperatures are reported.