Phase I of the Q/U Imaging ExperimenT (QUIET) measures the Cosmic Microwave Background polarization anisotropy spectrum at angular scales between 25 and 1000. QUIET has deployed two independent receiver arrays. The 40-GHz array took data between October 2008 and June 2009 in the Atacama Desert in northern Chile. The 90 GHz array was deployed in June 2009 and observations are ongoing. Both receivers observe four 15 x 15 degree regions of the sky in the southern hemisphere that are expected to have low or negligible levels of polarized foreground contamination. This thesis will describe the 40 GHz (Q-band) QUIET Phase I instrument, instrument testing, observations, analysis procedures, and preliminary power spectra.