The increasing demand for enantiomerically pure chemicals has stimulated extensive research into the preparation of heterogeneous chiral catalysts or separation media that combine both shape selectivity and enantioselectiviy(1). Helical pores in inorganic materials might be able to perform such functions, but their occurrence is rare(1). Attempts have been reported to synthesize a specific enantiomorph of the chiral zeolite beta(2), and chiral metal complexes have been used to assemble inorganic precursors into chiral frameworks(3,4) Materials with a fully three-dimensional array of helical structural units are particularly rare, because helical structures (such as quartz) are commonly generated by a uni-dimensional symmetry element acting on an achiral structural subunit(5,6). Here we report on a family of zeolite-type materials (which we call UCSB-7) that possess two independent sets of three-dimensional crosslinked helical pores, separated by a gyroid periodic minimal surface(13). We have synthesized the UCSB-7 framework for various compositions (zinc and beryllium arsenates, gallium germanate) using either inorganic cations or amines as structure-directing agents. The helical-ribbon motif that we identify might be exploited more widely for developing useful chiral solid-state structures.