The integration of materials having a high dielectric constant (high-kappa) into carbon-nanotube transistors promises to push the performance limit for molecular electronics. Here, high-kappa (similar to25) zirconium oxide thin-films (similar to8 nm) are formed on top of individual single-walled carbon nanotubes by atomic-layer deposition and used as gate dielectrics for nanotube field-effect transistors. The p-type transistors exhibit subthreshold swings of S similar to 70 mV per decade, approaching the room-temperature theoretical limit for field-effect transistors. Key transistor performance parameters, transconductance and carrier mobility reach 6,000 S m(-1) (12 muS per tube) and 3,000 cm(2) V-1 s(-1) respectively. N-type field-effect transistors obtained by annealing the devices in hydrogen exhibit S similar to 90 mV per decade. High voltage gains of up to 60 are obtained for complementary nanotube-based inverters. The atomic-layer deposition process affords gate insulators with high capacitance while being chemically benign to nanotubes, a key to the integration of advanced dielectrics into molecular electronics.