The effect of confinement on the dynamics of polymers was studied by observing the transient extension and relaxation of single DNA molecules as they interacted with obstacles in a specially designed thin slit. Viscous drag was found to increase with the degree of confinement, which we interpret in terms of hydrodynamic screening by the planar surfaces of the slit. Since the DNA was driven by an electrophoretic force, the experimental data support the notion that an electric field acts on a tethered polyelectrolyte equivalently to a hydrodynamic flow.