The Q/U Imaging ExperimenT (QUIET) employs coherent receivers at 43GHz and 95GHz, operating on the Chajnantor plateau in the Atacama Desert in Chile, to measure the anisotropy in the polarization of the CMB. QUIET primarily targets the B modes from primordial gravitational waves. The combination of these frequencies gives sensitivity to foreground contributions from diffuse Galactic synchrotron radiation. Between 2008 October and 2010 December, >10,000hours of data were collected, first with the 19-element 43GHz array (3458hours) and then with the 90-element 95GHz array. Each array observes the same four fields, selected for low foregrounds, together covering ~1000deg^2. This paper reports initial results from the 43GHz receiver which has an array sensitivity to CMB fluctuations of 69uK sqrt(s). The data were extensively studied with a large suite of null tests before the power spectra, determined with two independent pipelines, were examined. Analysis choices, including data selection, were modified until the null tests passed. Cross correlating maps with different telescope pointings is used to eliminate a bias. This paper reports the EE, BB and EB power spectra in the multipole range ell=25-475. With the exception of the lowest multipole bin for one of the fields, where a polarized foreground, consistent with Galactic synchrotron radiation, is detected with 3sigma significance, the E-mode spectrum is consistent with the LCDM model, confirming the only previous detection of the first acoustic peak. The B-mode spectrum is consistent with zero, leading to a measurement of the tensor-to-scalar ratio of r=0.35+1.06-0.87. The combination of a new time-stream double-demodulation technique, Mizuguchi-Dragone optics, natural sky rotation, and frequent boresight rotation leads to the lowest level of systematic contamination in the B-mode power so far reported, below the level of r=0.1
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