In this paper, we extend space-time block coding techniques, originally proposed for point-to-point communication links, to point-to-multipoint communication links, thereby taking into account the multiple access technique in the design of the transmission scheme. In specific, we propose two per-tone linear space-time chip equalizers for a space-time coded MC-DS-CDMA downlink with linear precoding. Both the training-based and the semi-blind chip equalizer exploit the presence of a continuous code-multiplexed pilot in the transmitted signal but differ in the amount of a-priori information they assume to estimate their coefficients. With Mt transmit antennas at the base-station, Mr receive antennas at the mobile station and L the order of the multipath channel, they come close to extracting the full diversity of order Mt · Mr · (L + 1) in reduced as well as full load settings.