The prospect of using low-temperature processable organic semiconductors to implement transistors, circuits, displays and sensors on arbitrary substrates, such as glass or plastics, offers enormous potential for a wide range of electronic products. Of particular interest are portable devices that can be powered by small batteries or by near-field radio-frequency coupling. The main problem with existing approaches is the large power consumption of conventional organic circuits, which makes battery-powered applications problematic, if not impossible. Here we demonstrate an organic circuit with very low power consumption that uses a self-assembled monolayer gate dielectric and two different air-stable molecular semiconductors (pentacene and hexadecafluorocopperphthalocyanine, F16CuPc). The monolayer dielectric is grown on patterned metal gates at room temperature and is optimized to provide a large gate capacitance and low gate leakage currents. By combining low-voltage p-channel and n-channel organic thin-film transistors in a complementary circuit design, the static currents are reduced to below 100 pA per logic gate. We have fabricated complementary inverters, NAND gates, and ring oscillators that operate with supply voltages between 1.5 and 3 V and have a static power consumption of less than 1 nW per logic gate. These organic circuits are thus well suited for battery-powered systems such as portable display devices and large-surface sensor networks as well as for radio-frequency identification tags with extended operating range.