Conducting tubes filled with neutral gas at pressures between 0.001 and 0.1 Torr can be used to transport, to center, and to reduce the transverse oscillations of high current (≳10 kA) electron beams. Electron impact ionization of the gas leads to partial neutralization of the beam space charge allowing self‐focused beam transport and phase‐mix damping of injected beam oscillations. In addition, the presence of conducting walls helps center the beam in the transport tube. High current beams, transported through a 1.3 m long tube, were centered to within one‐tenth of the beam radius and input transverse oscillations were damped to submillimeter values without significant current loss or emittance growth. Beam transport properties are examined as a function of injected current, gas pressure, and cell geometry. Experimental results are compared with a theoretical model.