We report measurements of anisotropy in the cosmic microwave background radiation over the multipole range l ~ 200 - 3500 with the Cosmic Background Imager based on deep observations of three fields. These results confirm the drop in power with increasing l first reported in earlier measurements with this instrument, and extend the observations of this decline in power out to l ~ 2000. The decline in power is consistent with the predicted damping of primary anisotropies. At larger multipoles, l = 2000 - 3500, the power is 3.1 sigma greater than standard models for intrinsic microwave background anisotropy in this multipole range, and 3.5 sigma greater than zero. This excess power is not consistent with expected levels of residual radio source contamination but, for sigma_8 >~ 1, is consistent with predicted levels due to a secondary Sunyaev-Zeldovich anisotropy. Further observations are necessary to confirm the level of this excess and, if confirmed, determine its origin.
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