The observation of the spin Hall effect triggered intense research on pure spin current transport. With the spin Hall effect, the spin Seebeck effect and the spin Peltier effect already observed, our picture of pure spin current transport is almost complete. The only missing piece is the spin Nernst (-Ettingshausen) effect, which so far has been discussed only on theoretical grounds. Here, we report the observation of the spin Nernst effect. By applying a longitudinal temperature gradient, we generate a pure transverse spin current in a Pt thin film. For readout, we exploit the magnetization-orientation-dependent spin transfer to an adjacent yttrium iron garnet layer, converting the spin Nernst current in Pt into a controlled change of the longitudinal and transverse thermopower voltage. Our experiments show that the spin Nernst and the spin Hall effect in Pt are of comparable magnitude, but differ in sign, as corroborated by first-principles calculations.