An experiment demonstrating the propagation of a 42‐MeV electron beam from an rf linear accelerator through 1 m of H2at pressures from 10−3to 1.25 atm is reported. Measurements were made of the transmitted current and the beam’s radius, transverse position, and angular divergence along the path. The beam current was fully transmitted at all pressures, without the often detrimental plasma interactions (space‐charge neutralization, magnetic neutralization, and various plasma instabilities) seen in previous studies. The observed beam expansion was consistent with calculations of multiple scattering. The propagation can be attributed to the 4‐ps duration of the accelerator’s electron bunches. This time is three to four orders of magnitude shorter than that used in the earlier work and is shorter than the growth times for the beam‐plasma interactions. Such a beam should prove suitable for a gas‐loaded free‐electron laser.