High precision ionization chambers were designed end built to measure the transverse spin dependence of the proton-proton total cross-section difference in the 318 MeV to 8 MeV energy region. Severe microphonic noise was minimized by mounting one of the chambers on pneumatic vibration isolators. Consideration of large fluctuations of the ionization produced in the thin gas layers of the chambers and the measured electronics noise accounts for about 6% of the resolution width of the measurement. Additional effects such as the beam intermittently scraping the target cavity, secondary emission of electrons, and beam-related RF pickup are postulated to account for the remaining width. Designing, constructing, and operation the high-precision ionization chambers has greatly improved our understanding of high-accuracy applications of ionization chambers and analog electronics.