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Superconducting qubits provide a competitive platform for quantum simulation of complex dynamics that lies at the heart of quantum many-body systems, because of the flexibility and scalability afforded by the nature of microfabrication. However, in a multiqubit device, the physical form of couplings between qubits is either an electric (capacitor) or magnetic field (inductor), and the associated quadratic field energy determines that only two-body interaction in the Hamiltonian can be directly realized. Here we propose and experimentally synthesize the three-body spin-chirality interaction in a superconducting circuit based on Floquet engineering. By periodically modulating the resonant frequencies of the qubits connected with each other via capacitors, we can dynamically turn on and off qubit-qubit couplings, and further create chiral flows of the excitations in the three-qubit circular loop. Our result is a step toward engineering dynamical and many-body interactions in multiqubit superconducting devices, which potentially expands the degree of freedom in quantum simulation tasks.