THE distribution of more than 150 gamma-ray bursts detected by the BATSE experiment is isotropic on the sky but radially nonuniform1,2. This raises the possibility that bursts are cosmological (at z less than or similar 1) and therefore very energetic events, releasing approximately 10(50) erg sr-1 on a timescale of seconds. The coalescence of two neutron stars 3-7 or the accretion-induced collapse of a white dwarf8 can release up to 10(53) erg in the form of neutrino-antineutrino pairs, so that the conversion of < 1% into gamma-rays by annihilation9 could generate gamma-ray bursts, but in all such models an optically thick wind tends to form10,11, preventing the gamma-rays from escaping and converting their energy into kinetic energy of the ejected material. We present here a possible solution to this difficulty. When a stellar-mass neutron star is disrupted by a black hole, it forms a thick disk which emits nunuBAR pairs. These neutrinos expel a wind from the disk, but angular momentum conservation means that a clear funnel forms along the rotation axis. Neutrino annihilation within the matter-free funnel can then create gamma-rays which escape to the distant observer.