We report the optical polarization of a gamma-ray burst (GRB) afterglow, obtained 203 seconds after the initial burst of gamma-rays from GRB 060418, using a ring polarimeter on the robotic Liverpool Telescope. Our robust (2sigma) upper limit on the percentage of polarization, less than 8%, coincides with the fireball deceleration time at the onset of the afterglow. The combination of the rate of decay of the optical brightness and the low polarization at this critical time constrains standard models of GRB ejecta, ruling out the presence of a large-scale ordered magnetic field in the emitting region.