Logic circuits and the ability to amplify electrical signals form the functional backbone of electronics along with the possibility to integrate multiple elements on the same chip. The miniaturization of electronic circuits is expected to reach fundamental limits in the near future. Two-dimensional materials such as single-layer MoS2 represent the ultimate limit of miniaturization in the vertical dimension, are interesting as building blocks of low-power nanoelectronic devices, and are suitable for integration due to their planar geometry. Because they are less than 1 nm thin, 2D materials in transistors could also lead to reduced short channel effects and result in fabrication of smaller and more power-efficient transistors. Here, we report on the first integrated circuit based on a two-dimensional semiconductor MoS2. Our integrated circuits are capable of operating as inverters, converting logical “1” into logical “0”, with room-temperature voltage gain higher than 1, making them suitable for incorporation into digital circuits. We also show that electrical circuits composed of single-layer MoS2 transistors are capable of performing the NOR logic operation, the basis from which all logical operations and full digital functionality can be deduced.