4 pages, 3 figures.-- Published in PRL: Phys.Rev.Lett. 98 (2007) 061302.-- Final full-text version of the paper available at: http://dx.doi.org/10.1103/PhysRevLett.98.061302.The process of reheating the universe after hybrid inflation is extremely violent. It proceeds through the nucleation and subsequent collision of large concentrations of energy density in bubble-like structures, which generate a significant fraction of energy in the form of gravitational waves. We study the power spectrum of the stochastic background of gravitational waves produced at reheating after hybrid inflation. We find that the amplitude could be significant for high-scale models, although the typical frequencies are well beyond what could be reached by planned gravitational wave observatories like LIGO, LISA or BBO. On the other hand, low-scale models could still produce a detectable stochastic background at frequencies accesible to those detectors. The discovery of such a background would open a new window into the very early universe.This work is supported in part by CICYT projects FPA2003-03801 and FPA2003-04597. D.G.F. also acknowledges support from a FPU Fellowship from the Spanish M.E.C.Peer reviewed