We report on a study of the Seebeck coefficient and resistivity in the quasi-one-dimensional conductor (TMTSF)2 PF6 extended deep into the spin-density-wave state. The metal-insulator transition at TSDW=12 K leads to a reduction in carrier concentration by 7 orders of magnitude. Below 1 K, charge transport displays the behavior known as variable range hopping. Until now, the Seebeck response of electrons in this regime has barely been explored and is even less understood. We find that, in this system, residual carriers, hopping from one trap to another, generate a Seebeck coefficient as large as 400 kB/e. The results provide the first solid evidence for a long-standing prediction according to which hopping electrons in the presence of the Coulomb interaction can generate a sizable Seebeck coefficient in the zero-temperature limit.