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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, which is the Sunyaev-Zel'dovich (SZ) effect. We estimate the density fluctuation parameters for amplitude, σ 8, and shape, Γ, from CMB primary anisotropy data and other cosmological data. We use the results of two separate hydrodynamic codes for ΛCDM cosmologies, consistent with the allowed σ 8 and Γ values, to quantify the expected contribution from the SZ effect to the band powers of the CBI experiment and pass simulated SZ effect maps through our CBI analysis pipeline. The result is very sensitive to the value of σ 8 and is roughly consistent with the observed …