Transient and steady elongational viscosity has been measured for two narrow molar mass distribution polystyrene melts of molar masses 200 000 and 390 000 by means of a filament stretching rheometer. Total Hencky strains of about five have been obtained. The transient elongational viscosity rises above the linear viscoelastic prediction at intermediate strains, indicating strain hardening. The steady elongational viscosities are monotone decreasing functions of elongation rate. At elongation rates larger than the inverse reptation time, the steady elongational viscosity scales linearly with molar mass at fixed elongation rate.