We report on the unexpected finding of nanoscale fibers with a diameter down to 25 nm that emerge from a polymer solution during a standard spin-coating process. The fiber formation relies upon the Raleigh-Taylor instability of the spin-coated liquid film that arises due to a competition of the centrifugal force and the Laplace force induced by the surface curvature. This procedure offers an attractive alternative to electrospinning for the efficient, simple, and nozzle-free fabrication of nanoscale fibers from a variety of polymer solutions.