Self-organization in many solution-processed, semiconducting conjugated polymers results in complex microstructures, in which ordered microcrystalline domains are embedded in an amorphous matrix. This has important consequences for electrical properties of these materials: charge transport is usually limited by the most difficult hopping processes and is therefore dominated by the disordered matrix, resulting in low charge-carrier mobilities (≤10-5 cm2V-1s-1). Here we use thin-film, field-effect transistor structures to probe the transport properties of the ordered microcrystalline domains in the conjugated polymer poly(3-hexylthiophene), P3HT. Self-organization in P3HT results in a lamella structure with two- dimensional conjugated sheets formed by interchain stacking. We find that, depending on processing conditions, the lamellae can adopt two different orientations - parallel and normal to the substrate - the mobilities of which differ by more than a factor of 100, and can reach values as high as 0.1 cm2 V-1 s-1 (refs 3, 4). Optical spectroscopy of the field-induced charge, combined with the mobility anisotropy, reveals the two-dimensional interchain character of the polaronic charge carriers, which exhibit lower relaxation energies than the corresponding radical cations on isolated one-dimensional chains. The possibility of achieving high mobilities via two-dimensional transport in self-organized conjugated lamellae is important for applications of polymer transistors in logic circuits and active-matrix displays.