Electron-capture spectroscopy has been used to investigate magnetic order at the topmost atomic layer of atomically clean and flat (100) surfaces of bulk paramagnetic vanadium. From low-energy electron diffraction measurements, we find a p(1×1) surface structure. At 300 K, the long-ranged electron-spin polarization amounts to ∼34%, clearly demonstrating the existence of ferromagnetic order at the V(100) p(1×1) surface. With increasing temperature, the electron-spin polarization decreases almost linearly and disappears at a surface Curie temperature TCs≈540 K.