The pure rotational spectrum of BaNH in its X 1 Σ + ground electronic state has been recorded using millimeter/submillimeter direct absorption methods; data for the deuterium and barium 137 isotopomers have been measured as well. The molecules were produced by the reaction of ammonia or ND3 and barium vapor in the presence of a dc discharge. Transitions arising from the ground vibrational state and the excited vibrational bending (01 1 0) and heavy atom stretching (100) modes were measured. The rotational spectrum indicates a linear structure, with B0(BaNH) ) 7984.549 MHz and B0(BaND) ) 7060.446 MHz. An rm (1) structure has been determined, yielding r(BaN) ) 2.077 ( 0.002 Å and r(NH) ) 1.0116 ( 0.0006 Å. Density functional calculations using an extensive Slater-type basis set with inclusion of scalar relativistic effects gives geometrical parameters and vibrational frequencies for BaNH in excellent agreement with those determined by experiment. The molecular orbital and natural bond order analyses of the BaNH wave function show Ba-N π bonds formed by electron donation from the formally filled N 2p orbitals of the imido group to the empty Ba 5d orbitals. The multiple bonding between Ba and N stabilizes the linear geometry and, along with the relative ease of oxidation of the Ba atom, favors formation of the metal-imido species over that of the metal-amido species that have been found from similar studies with Mg, Ca, and Sr atoms in this group.