We investigate the rheological behavior of Langmuir monolayers consisting of polyisoprene chains tethered by one end to the air/water interface. These 10-50 nm thick monolayers provide model systems of a molten polymer brush for which the ends can move within the interface. Their linear viscoelastic properties are determined by applying a small-amplitude shear flow within the interface plane and investigated as a function of surface density and length of tethered chains. When increasing the chain length, we observe a transition from a liquidlike to a transient network behavior typical of entangled bulk polymer melts. The terminal relaxation time and the effective bulk zero shear viscosity of the monolayers are 2-3 orders of magnitude higher than those of a linear bulk polyisoprene melt of identical molecular weight. Both quantities are shown to exhibit an enhanced molecular weight dependence and to increase with surface density.