The A˜2Πr (000)←X˜2Σ+ (000) system of a cold beam of barium hydroxide, BaOH, has been studied field-free and in the presence of a static electric field. Stark tuning of the low-J branch features in the A˜2Π3/2 (000)←X˜2Σ+ (000) transition were analyzed to give permanent electric dipole moments, μ, for the A˜2Π3/2 (000) and X˜2Σ+ (000) states of 0.477(7) D and 1.43(4) D, respectively. The results are compared with other alkaline earth monohydroxides and values predicted using an electrostatic polarization model and ligand field theory.