Field effect conductance measurements were made on individual microscopic crystals of the organic semi-conductor sexithiophene (6T). These crystals, ranging from 1 to 6 molecules (2-14 nm) in thickness and from 1 to 2 mu m in diameter, were deposited by thermal evaporation onto SiO2 substrates previously patterned with closely spaced (similar to 400 nm) pairs of Au wires. Atomic force microscopy (AFM) of these substrates demonstrated the growth of individual 6T crystals between the wires. The resulting wire/6T/wire structures were used in a transistor configuration to probe the in-plane conductance of the crystals as a function of transverse electric field (i.e., perpendicular to the substrate). These measurements showed (1) no discernible dependence of the carrier mobility on thickness - even down to crystals as thin as a monolayer-suggesting that much of the current is carried by the first monolayer next to the SiO2, (2) activated transport (E-A = 25 meV) at temperatures above 100 K but nearly temperature-independent transport from 5 to 100 K, and (3) slowly decaying currents associated with reversible charge trapping. In cases where two crystals were isolated between Au electrodes, the resultant grain boundary severely limited conduction. In general, we have developed a reproducible method for electrically contacting two-dimensional molecular assemblies and have demonstrated the utility of transport measurements, in combination with AFM imaging, for elucidating structure-transport relationships in organic materials.