We measure hydrodynamic interactions between colloidal particles confined in a thin sheet of fluid. The reduced dimensionality, compared to a bulk fluid, increases dramatically the range of couplings. Using optical tweezers we force a two body system along the eigenmodes of the mobility tensor and find that eigenmobilities change logarithmically with particle separation. At a hundred radii distance, the mobilities for rigid and relative motions differ by a factor of 2, whereas in bulk fluids, they would be practically indistinguishable. A two dimensional counterpart of Oseen hydrodynamic tensor quantitatively reproduces the observed behavior, once the relevant boundary conditions are recognized. These results highlight the importance of dimensionality for transport and interactions in colloidal systems and proteins in biological membranes.