We discuss the nature of the possible high-l excess in the Cosmic Microwave Background (CMB) anisotropy power spectrum observed by the Cosmic Background Imager (CBI). We probe the angular structure of the excess in the CBI deep fields and investigate whether it could be due to the scattering of CMB photons by hot electrons within clusters, the Sunyaev-Zeldovich (SZ) effect. We estimate the density fluctuation parameters for amplitude, sigma_8, and shape, Gamma, from CMB primary anisotropy data and other cosmological data. We use the results of two separate hydrodynamical codes for Lambda-CDM cosmologies, consistent with the allowed sigma_8 and Gamma values, to quantify the expected contribution from the SZ effect to the bandpowers of the CBI experiment and pass simulated SZ effect maps through our CBI analysis pipeline. The result is very sensitive to the value of sigma_8, and is roughly consistent with the observed power if sigma_8 ~ 1. We conclude that the CBI anomaly could be a result of the SZ effect for the class of Lambda-CDM concordance models if sigma_8 is in the upper range of values allowed by current CMB and Large Scale Structure (LSS) data.