According to quantum mechanics, chiral states cannot be non-degenerate eingenstates of a parity-conserving Hamiltonian. This is in contradiction to the existence of chiral molecules—a fact known as as the Hund paradox¹. The origin of molecular and biological chirality is conjectured to be related to parity-breaking interactions^2,3 or environmental decoherence⁴, but a quantum superposition of two chiral molecular states with distinctive optical activities has never been observed⁵. To make progress in addressing these questions, it would be helpful to construct an artificial quantum system that breaks the parity symmetry and that can be prepared in a superposition of two chiral states. Here we report the synthesis of the parity-breaking antisymmetric spin exchange interaction in all-to-all connected superconducting circuits, which allows us to show various chiral spin dynamics in up to five-spin clusters. We also demonstrate the entanglement of up to five qubits in Greenberger–Horne–Zeilinger states based on a three-spin chiral logic gate. Our results are a step towards quantum simulation of magnetism with antisymmetric spin exhange interaction and quantum computation with chiral spin states.