By a combined angle-resolved photoemission spectroscopy and density functional theory study, we discover that the surface metallicity is polarity driven in SmB6. Two surface states, not accounted for by the bulk band structure, are reproduced by slab calculations for coexisting B6 and Sm surface terminations. Our analysis reveals that a metallic surface state stems from an unusual property, generic to the (001) termination of all hexaborides: the presence of boron 2p dangling bonds, on a polar surface. The discovery of polarity-driven surface metallicity sheds new light on the 40-year old conundrum of the low-temperature residual conductivity of SmB6, and raises a fundamental question in the field of topological Kondo insulators regarding the interplay between polarity and nontrivial topological properties.