Clouds of electrons in the vacuum chambers of accelerators of positively charged particle beams present a serious limitation for operation of these machines at high currents. Because of the size of these accelerators, it is difficult to probe the low energy electron clouds over substantial lengths of the beam pipe. We applied a novel technique to directly measure the electron cloud density via the phase shift induced in a TE wave which is independently excited and transmitted over a straight section of the accelerator. The modulation in the wave transmission which appear to increase in depth when the clearing solenoids are switched off, seem to be directly correlated to the electron cloud density in the section. Furthermore, we expect a larger phase shift of a wave transmitted through magnetic dipole field regions if the transmitted wave couples with the gyration motion of the electrons. We have used this technique to measure the average electron cloud density (ECD) specifically for the first time in magnetic field regions of a new 4-dipole chicane in the positron ring of the PEP-II collider at SLAC. In this paper we present and discuss the measurements taken in the Low Energy Ring (LER) between 2006 and 2008. Show Partial Abstract