  In an ideal classical pyrochlore antiferromagnet without perturbations, an
infinite degeneracy at a ground state leads to absence of a magnetic order and
spin-glass transition. Here we present Na$_3$Mn(CO$_3$)$_2$Cl as a new
candidate compound where classical spins are coupled antiferromagnetically on
the pyrochlore lattice, and report its structural and magnetic properties.The
temperature dependences of the magnetic susceptibility and heat capacity, and
the magnetization curve are consistent with those of an $S$ = 5/2 pyrochlore
lattice antiferromagnet with nearest-neighbor interactions of 2 K. Neither an
apparent signature of a spin-glass transition nor a magnetic order is detected
in magnetization and heat capacity measurements, or powder neutron diffraction
experiments. On the other hand, an antiferromagnetic short-range order from the
nearest neighbors is evidenced by the $Q$-dependence of the diffuse scattering
which develops around 0.85 \AA$^{-1}$. A high degeneracy near the ground state
in Na$_3$Mn(CO$_3$)$_2$Cl is supported by the magnetic entropy estimated as
almost 4 J K$^{-2}$ mol$^{-1}$ at 0.5 K.
