An integral solution to the quantum Knizhnik - Zamolodchikov (qKZ) equation with |q|=1 is presented. Upon specialization, it leads to a conjectural formula for correlation functions of the XXZ model in the gapless regime. The validity of this conjecture is verified in special cases, including the nearest-neighbour correlator with an arbitrary coupling constant and general correlators in the XXX and XY limits.