[en] We describe the construction and behaviour of a set of cylindrical drift chambers operating inside a superconducting solenoid with a central magnetic field of 1.3 T. The chambers are part of the 4 π detector CELLO at the e⁺e^- storage ring PETRA in Hamburg. The chambers were designed without field shaping to keep them as simple as possible. In order to parametrize accurately the nonlinear space-time relation, we used a computer simulation of the drift process in inhomogenous electric and magnetic fields. With such a parametrization we achieved a resolution of 210 μm, averaged over the whole drift cell and angles of incidence up to 30⁰. (orig.)