In this paper, we present an efficient LMMSE chip equalizer to suppress the interference caused by the multipath fading channel in the MIMO multi-code CDMA downlink. The block-Toeplitz structure in the correlation matrix is approximated with a block circulant matrix. An FFT-based algorithm is applied to avoid the Direct-Matrix-Inverse (DMI) in the system equation. Hermitian optimization is proposed to further reduce the complexity. A comparative study in both performance and complexity with the Conjugate-Gradient (CG) algorithm is then presented. The simulation shows very promising results for the FFT-based equalizer compared with both the DMI and CG algorithms.