Lanthanide hydroxides are key species in a variety of catalytic processes and in the preparation of corresponding oxides. This work explores the fundamental structure and bonding of the simplest lanthanide hydroxide, LnOH (Ln=La-Lu), using density functional theory calculations. Interestingly, the calculations predict that all structures of this series will be linear. Furthermore, these results indicate a valence electron configuration featuring an occupied sigma orbital and two occupied pi orbitals for all LnOH compounds, suggesting that the lanthanide-hydroxide bond is best characterized as a covalent triple bond.