We propose and investigate the intrinsically thinnest transistor concept: a monolayer ballistic heterojunction bipolar transistor based on a lateral heterostructure of transition metal dichalcogenides. The device is intrinsically thinner than a Field Effect Transistor because it does not need a top or bottom gate, since transport is controlled by the electrochemical potential of the base electrode. As typical of bipolar transistors, the collector current undergoes a tenfold increase for each 60 mV increase of the base voltage over several orders of magnitude at room temperature, without sophisticated optimization of the electrostatics. We present a detailed investigation based on self-consistent simulations of electrostatics and quantum transport for both electron and holes of a pnp device using MoS2 for the 10-nm base and WSe2 for emitter and collector. Our three-terminal device simulations confirm the working principle and a large current modulation ION/IOFF∼108 for ΔVEB=0.5 V. Assuming ballistic transport, we are able to achieve a current gain β∼ 104 over several orders of magnitude of collector current and a cutoff frequency up to the THz range. Exploration of the rich world of bipolar nanoscale device concepts in 2D materials is promising for their potential applications in electronics and optoelectronics.