We present 30 GHz measurements of the angular power spectrum of the cosmic microwave background (CMB) obtained with the Sunyaev-Zeldovich Array. The measurements are sensitive to arcminute angular scales, where secondary anisotropy from the Sunyaev-Z
eldovich effect (SZE) is expected to dominate. For a broad bin centered at multipole 4066 we find 67+77-50 uK^2, of which 26+/-5 uK^2 is the expected contribution from primary CMB anisotropy and 80+/-54 uK^2 is the expected contribution from undetected radio sources. These results imply an upper limit of 155 uK^2 (95% CL) on the secondary contribution to the anisotropy in our maps. This level of SZE anisotropy power is consistent with expectations based on recent determinations of the normalization of the matter power spectrum, i.e., sigma_8~0.8.
