  The cross section for the thermal neutron capture by the deuteron is
calculated with pionless Effective Field Theory(EFT). No new Three-Nucleon
forces are needed up to next-to-next-to-leading order in order to achieve
cut-off independent results, besides those fixed by the triton binding energy
and Nd scattering length in the triton channel. The cross-section is accurately
determined to be $\sigma_{tot}=[0.503\pm 0.003]mb$. At zero energies, the
magnetic $M1$-transition gives the dominant contribution and is calculated up
to next-to-next-to-leading order (N$^2$LO). Close agreement between the
available experimental data and the calculated cross section is reached. We
demonstrate convergence and cutoff independence order by order in the
low-energy expansion.
