  We report on a study of Seebeck coefficient and resistivity in the
quasi-one-dimensional conductor (TMTSF)$_{2}$PF$_{6}$ extended deep into the
Spin-Density-Wave(SDW) state. The metal-insulator transition at $T_{SDW}$ = 12
K leads to a reduction in carrier concentration by seven orders of magnitude.
Below 1 K, charge transport displays the behavior known as Variable Range
Hopping (VRH). Until now, the Seebeck response of electrons in this regime has
been barely explored and 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 $k_{B}$/$e$. The results provide the first solid
evidence for a long-standing prediction according to which hopping electrons in
presence of Coulomb interaction can generate a sizeable Seebeck coefficient in
the zero-temperature limit.
