The effects of edge chemistry on the relative stability and electronic properties of zigzag boron nitride nanoribbons (ZBNNRs) are investigated. Among all functional groups considered, fully hydroxylated ZBNNRs are found to be the most energetically stable. When an in-plane external electric field is applied perpendicular to the axis of both hydrogenated and hydroxylated ZBNNRs, a spin-polarized half-metallic state is induced, whose character is different than that predicted for zigzag graphene nanoribbons. The onset field for achieving the half-metallic state is found to mainly depend on the width of the ribbon. Our results indicate that edge functionalization of ZBNNRs may open the way for the design of new nanoelectronic and nanospintronic devices.