  Topological insulators are guaranteed to support metallic surface states on
an insulating bulk, and one should thus expect that the electronic transport in
these materials is dominated by the surfaces states. Alas, due to the high
remaining bulk conductivity, surface contributions to transport have so-far
only been singled out indirectly via quantum oscillations, or for devices based
on gated and doped topological insulator thin films, a situation in which the
surface carrier mobility could be limited by defect and interface scattering.
Here we present the first direct measurement of surface-dominated conduction on
an atomically clean surface of bulk-insulating Bi$_2$Te$_2$Se. Using nano-scale
four point setups with variable contact distance, we show that the transport at
30 K is two-dimensional rather than three-dimensional and by combining these
measurements with angle-resolved photoemission results from the same crystals,
we find a surface state mobility of 390(30) cm$^{2}$V$^{-1}$s$^{-1}$ at 30 K at
a carrier concentration of 8.71(7)$\times 10^{12}$ cm$^{-2}$.
