We consider stimulated Brillouin scattering excited in a "feedback-free" optical fiber by continuous wave monochromatic pump radiation. We show the Stokes signal displays stochastic dynamic behavior from its onset. On increase of the pump signal a window of periodicity emerges from and subsequently subsides into the stochastic emission, the period of which corresponds to the round-trip time in the fiber. We show this feature arises from coherent regenerative amplification of the stochastic spontaneous Brillouin scattering due to minute residual feedback. © 2008 The American Physical Society.