Clouds of low energy electrons in the vacuum beam pipes of accelerators of positively charged particle beams present a serious limitation for operation at high currents. Furthermore, it is difficult to probe their density over substantial lengths of the beam pipe. We have developed a novel technique to directly measure the electron cloud density via the phase shift induced in a TE wave transmitted over a section of the accelerator and used it to measure the average electron cloud density over a 50 m section in the positron ring of the PEP-II collider at the Stanford Linear Accelerator Center.