  We study positional coincidences between gamma-ray bursts in the BATSE 3B
catalogue and quasars/AGN taken from the Veron-Cetty & Veron compilation. For
most classes of AGN, for BL Lac objects and for radio-loud quasars, we find no
excess coincidences above random expectation, and we give upper limits for
their burst emission rate. However, surprising evidence is found for a
positional correlation between gamma-ray bursts and radio-quiet quasars. A
total of 134 selected bursts with a position error radius <1.8d and the nearest
and intrinsically brightest radio-quiet quasars (M_v<-24.2 and z<1.0) have a
probability of >99.7% to be associated with each other. An analysis of a
smaller sample of well-localized interplanetary network gamma-ray burst
positions supports this result. This correlation strongly favours the
cosmological origin of gamma-ray bursts and enables to estimate its distance
scale. The average luminosity of those gamma-ray bursts which we associate
directly with radio-quiet quasars is of the order of 4*10^52 erg (assuming
isotropic emission).
