The rational design of mechanical metamaterials endows them with unusual properties inaccessible by conventional materials. In this study, compression–twist coupling building blocks with embedded chirality are fabricated by multimaterial 4D printing of shape memory polymers. Each chiral unit can be programmed individually by mechanical compression at a selected high temperature, whose temporary shape is self-maintained at the reduced temperature when the load is removed. With these building blocks, lattice-like architectures can be constructed in planar and layer-to-layer assemblies. Such modular design overcomes the limitation of conventional material arrangement by allowing on-demand re-programmability of chirality-defined structural heterogeneity. Using this strategy, metamaterials with tunable Poisson's ratio and shape-morphing metastructures are developed by harnessing the cooperative deformation of spatially heterogenous tessellation that undergoes local shrinkage or expansion, depending on the encoded Poisson response. An untethered multimodal soft gripper is assembled by chiral metastructures with distinct morphing modes, capable of unscrewing up a bottle cap attributed by the programmed functionality at module-level. The present modular chiral metamaterials with embedded chirality and flexible deployability may promote the applications of mechanical metamaterials in active shape-morphing structures and functional soft machines.