A novel technique to create a vacuum pump on an integrated circuit chip is presented. This pump consists of small tubes operating in the free molecular flow regime, connected to larger, although still miniature, viscous flow chambers. The gas is alternately heated and cooled as it traverses these tubes and chambers, the thermal transpiration effect creating a mass flow and compression in each stage. The pump has no moving parts, eliminating wear and particulate generation and increasing reliability, also the power required is low, in the milliwatt range, permitting battery power for portability; no valves are required; and the pump is silent, with no noise being generated. An analysis is given for sizing the dimensions of the free molecular tubes and the continuum cells. Two examples are provided for a vacuum pump compressing from 3 up to 152 Torr at flow rates of 2E-4 and 2E-3 sccm, the latter case having the connecting tubes in transition (Knudsen number of 1). These parameters are appropriate for the first roughing pump of a “mass spectrometer on a chip” gas sensor.