Anomalous optical birefringence and optical rotation have been observed in a liquid crystal phase comprising of W-shaped liquid crystal molecules with hydrogen bonds. The texture of this phase exhibits characteristic chiral filaments, which form strongly segregated chiral domains similar to the B4 phase of conventional bent-core mesogens, despite of having no chiral carbon. Based on X-ray microbeam diffraction, polarizing and confocal optical microscope observations, the molecular arrangement in the filament is discussed, and the novel structure different from that in B4 is proposed; the smectic layers form concentric cylinder, on which the c-director of the W- shaped molecules form screw-like and/or polar arrangement, inducing herringbone anisotropic structure and chirality in each filament, as observed in the experiments.