A population of 30 MeV runaway electrons in the TEXTOR tokamak is diagnosed by their synchrotron emission. During pellet injection a large fraction of the population is lost within 600 mus. This rapid loss is attributed to stochastization of the magnetic field. The remaining runaways form a narrow, helical beam at the q = 1 drift surface. The radial and poloidal diffusion of this beam is extremely slow, D < 0.02 m2/s. The fact that the beam survives the period of stochastic field shows that in the chaotic sea big magnetic islands must remain intact.