Compliant cellular structures are good candidates for morphing applications. This paper proposes a novel chiral cellular structure composed of circular beams with great elastic properties and potential for morphing. The tensile and shear elastic properties of the structure are studied through theoretical derivations and then verified by finite element analysis. Results show that this novel chiral structure exhibits extremely low in-plane tensile and shear moduli, which are many orders of magnitude lower than that of the raw material. The structure also shows tensile–shear and shear–tensile coupling effects that cannot be ignored. The tensile and shear properties of the structure can provide a reference for employing this structure in engineering applications.