Extremely thin, single crystals of sexithiophene (6T), 2–14 nm thick and 2–5 μm in length and width, can be grown an flat gold substrates by thermal evaporation. The thickness dimension corresponds to 1–6 monolayers (ML) of 6T molecules arranged with their long axes nearly perpendicular to the substrate. We have measured the current-voltage (I-V) characteristics through the thickness of these crystallites, after doping them with iodine, using conducting probe atomic force microscopy (CPAFM). The I-V traces are linear in the ±50 mV regime. The conductance (I/V) of the doped 6T crystals does not decrease monotonically with increasing thickness as might be expected, but instead has a maximum at 3 ML thickness, and we discuss several possible explanations for this observation.