  The cross section for radiative thermal neutron capture on ${}^{3}He$ ($\He3
+n \to \He4 +\gamma$; known as the $hen$ reaction) is calculated based on
heavy-baryon chiral perturbation theory. The relevant M1 operators are derived
up to next-to-next-to-next-to-leading order (N${}^3$LO). The initial and final
nuclear wave functions are obtained from the rigorous Faddeev-Yakubovski
equations for five sets of realistic nuclear interactions. Up to N${}^3$LO, the
M1 operators contain two low-energy constants, which appear as the coefficients
of non-derivative two-nucleon contact terms. After determining these two
constants using the experimental values of the magnetic moments of the triton
and ${}^3 He$, we carry out a parameter-free calculation of the $hen$ cross
section. The results are in good agreement with the data.
