We report the formation of the chiral quantum droplet in a spin-orbit-coupled Bose gas, where the system turns to a self-bound droplet when moving towards a particular direction and remains gaseous otherwise. The chirality arises from the breaking of Galilean invariance by spin-orbit coupling, which enables the system to dynamically adjust its condensation momentum and spin polarization in response to its velocity. As a result, only towards a specific moving direction and beyond a critical velocity, the acquired spin polarization can trigger collective interactions sufficient for self-binding and drive a first-order transition from gas to droplet. We map out a phase diagram of the droplet, gas, and their coexistence for realistic spin-orbit-coupled ${}^{39}\mathrm{K}$ mixtures with tunable moving velocity and magnetic detuning. Our results reveal the emergence of chirality in spin-orbit-coupled quantum gases, which shed light on general chiral phenomena in moving systems with broken Galilean invariance.

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• Bose gases
• Bose-Einstein condensates
• Cold atoms & matter waves
• Spin-orbit coupling