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We report upper limits on the polarization of the CMBR as measured with theCosmic Background Imager, a 13 element interferometer that operates in the26-36 GHz band and is sited on Llano de Chajnantor in northern Chile. The arrayconsists of 90-cm Cassegrain antennas mounted on a steerable platform that canbe rotated about the optical axis to facilitate polarization observations. TheCBI employs single-mode circularly polarized receivers and it samplesmultipoles from l~400 to l~3500. The polarization data were calibrated on 3C279and Tau A. The polarization observations consist of 278 hours of data on twofields taken in 2000, during the first CBI observing season. A joint likelihoodanalysis of the two fields yields three upper limits (95% c.l.) for\mathcal{C}_l^{EE} = C^{EE}l(l+1)/(2pi) under the assumption that\mathcal{C}_l^{BB}=0: 49.0 microK^2 (l=603); 164 microK^2 (l=1144); and 630microK^2 (l=2048).Comment: 17 pages, 3 figures, scheduled for 10 April 2005 Ap

Limits on the Polarization of the Cosmic Microwave Background Radiation at Multipoles up tol∼ 2000