Organic thin film transistors (TFTs) are of interest for a variety of large-area electronic applications, such as displays, sensors and electronic barcodes. One of the key problems with existing organic TFTs is their large operating voltage, which often exceeds 20 V. This is due to poor capacitive coupling through relatively thick gate dielectric layers: these dielectrics are usually either inorganic oxides or nitrides, or insulating polymers, and are often thicker than 100 nm to minimize gate leakage currents. Here we demonstrate a manufacturing process for TFTs with a 2.5-nm-thick molecular self-assembled monolayer (SAM) gate dielectric and a high-mobility organic semiconductor (pentacene). These TFTs operate with supply voltages of less than 2 V, yet have gate currents that are lower than those of advanced silicon field-effect transistors with SiO2 dielectrics. These results should therefore increase the prospects of using organic TFTs in low-power applications (such as portable devices). Moreover, molecular SAMs may even be of interest for advanced silicon transistors where the continued reduction in dielectric thickness leads to ever greater gate leakage and power dissipation.