The synthesis of crystalline molecular sieves with pore dimensions that fill the gap between microporous and mesoporous materials is a matter of fundamental and industrial interest1, 2, 3. The preparation of zeolitic materials with extralarge pores and chiral frameworks would permit many new applications. Two important steps in this direction include the synthesis4 of ITQ-33, a stable zeolite with 18 10 10 ring windows, and the synthesis5 of SU-32, which has an intrinsically chiral zeolite structure and where each crystal exhibits only one handedness. Here we present a germanosilicate zeolite (ITQ-37) with extralarge 30-ring windows. Its structure was determined by combining selected area electron diffraction (SAED) and powder X-ray diffraction (PXRD) in a charge-flipping algorithm6. The framework follows the SrSi2 (srs) minimal net7 and forms two unique cavities, each of which is connected to three other cavities to form a gyroidal channel system. These cavities comprise the enantiomorphous srs net of the framework. ITQ-37 is the first chiral zeolite with one single gyroidal channel. It has the lowest framework density (10.3 T atoms per 1,000 Å3) of all existing 4-coordinated crystalline oxide frameworks, and the pore volume of the corresponding silica polymorph would be 0.38 cm3 g-1.