Dedicated to K. Dransfeld on the occasion of his 60th birthdayThe electrical conductivity of a iodine-doped polyacetylene is measured as a function of the electric field C at temperatures between 4 K and 0.3 K. We find that after an initial non-linear behavior a increases linearly with ~ in agreement with a theoretical description based on variable-range hopping conduction. The non-linear rise at low fields depends on the iodine concentration. In heavily doped samples the increase is small and varies as g2, whereas in less conductive samples a large change is observed at 0.3 K which varies approximately as logd ~ for fields from 1 V/m to 150 V/m.