Lab-on-a-chip devices have a tremendous potential in a variety of fields, because of the possibility that these devices offer to control the fate of chemical and biological species. We study the use of chemically patterned surfaces to achieve vector separation of particles in microfluidic devices. In particular, we consider the case in which the pattern consists of two chemically different stripes arranged periodically. In the absence of external forces, the distribution will be homogeneous within each stripe and the particles will partition according to their interaction with the pattern. The concentration of a given particle will be higher on the region with higher particle-surface affinity. We investigate the chromatographic angle at which different species move under the action of a force, which can be due either to an externally applied field or to the hydrodynamic drag of a flow field. At steady state, the total flux will be constant to satisfy mass conservation. The convective flux differs in the two regions because of the concentration difference due to partitioning. To satisfy the continuity of the total flux, a concentration gradient and the ensuing diffusive flux must arise to compensate for the difference in the convective flux. The diffusive flux due to the concentration gradient results in an average particle trajectory angle that differs, in general, from the external force orientation angle. We solve analytically the particle transport equations and arrive at expressions for the trajectory angle and the dispersivity in terms of the external force orientation angle, the partition coefficient, the Peclet number, and the width of each stripe. We show that differences in the partition coefficient for different species leads to vector separation. Experimental measurements of the equilibrium partition coefficient and of the chromatographic trajectory angle will be presented and compared with the theoretical predictions