We present thermodynamic and neutron data on Ni3V2O8, a spin-1 system on a kagomé staircase. The extreme degeneracy of the kagomé antiferromagnet is lifted to produce two incommensurate phases at finite T—one amplitude modulated, the other helical—plus a commensurate canted antiferromagnet for T→0. The H−T phase diagram is described by a model of competing first and second neighbor interactions with smaller anisotropic terms. Ni3V2O8 thus provides an elegant example of order from subleading interactions in a highly frustrated system.