We present a resistance bridge which uses a SQUID to measure the shot noise in low impedance samples. The experimental requirements are high DC bias currents (typically 10mA) together with high AC sensitivity (pA/VHz). This system is used to investigate the shot noise in Superconductor/Normal/Superconductor junctions where Andreev reflection enhanced shot noise is expected. Because our setup has an intrinsic noise much smaller than the thermal noise of the resistance bridge at 4.2K, reliable results can be obtained on impedances out of the range of classical measurement schemes.