The mechanics of phase transforming cellular materials (PXCMs) with three different chiral honeycomb architectures, viz., hexachiral, tetra-anti-chiral, and tetra-chiral, are investigated under quasi-static loading/unloading. Each PXCM comprises interconnected unit cells consisting of tape springs rigidly affixed to circular nodes that can rotate and/or translate. The phase change is associated with snap-through instability due to bending of the tape springs and corresponds to sudden changes in the geometry of the unit cells from one stable configuration to another stable (or metastable) configuration during loading/unloading. When compared with similar chiral materials with flat ligaments, the chiral PXCMs exhibit a significantly higher energy dissipation in quasi-static experiments. The hexachiral PXCM was selected for detailed parametric analysis with finite element simulations including 21 models constructed to investigate the effects of PXCM geometry on phase change and energy dissipation. An analytical formalism is developed to predict the minimum compressive load required to induce phase transformation and snap-through. The formalism predictions are compared with those from finite element simulations. An Ashby plot is developed in which the energy dissipated per unit volume versus work conjugate plateau stress of the H-PXCM is compared with other energy absorbing materials.