Quantum spin fluctuation in a low-dimensional or frustrated magnet breaks magnetic ordering while keeping spin correlation. Such fluctuation has been a central topic in magnetism because of its relevance to high-T c superconductivity and topological states. However, utilizing such spin states has been quite difficult. In a one-dimensional spin-1/2 chain, a particle-like excitation called a spinon is known to be responsible for spin fluctuation in a paramagnetic state. Spinons behave as a Tomonaga-Luttinger liquid at low energy, and the spin system is often called a quantum spin chain. Here we show that a quantum spin chain generates and carries spin current, which is attributed to spinon spin current. This is demonstrated by observing an anisotropic negative spin Seebeck effect along the spin chains in Sr 2 CuO 3. The results show that spin current can flow even in an atomic channel owing to long-range spin fluctuation.