In this paper, we consider block spread code division multiple access (BS-CDMA) systems using Chu sequences as the spreading codes, namely the ChuBS-CDMA systems, and study the percoder design for such systems. We show that Chu-BS-CDMA using the conventional zero-padding precoder and minimum mean squared error (MMSE) detector yields an inferior performance, while that using the existing optimal S-precoder with successive detection yields a substantial performance gain with a high computational complexity. To combat the disadvantages occurred in the aforementioned two types of precoders, we propose in this paper a novel suboptimal precoder design, where ChuBS-CDMA using the proposed precoder and decoder and successive detection is shown to achieve a performance comparable to that using the optimal S-precoder, while offering a much reduced complexity. In particular, the design of optimal S-precoder requires channel state information (CSI) and iterative eigen-value decompositions at the transmitter, while the proposed precoder and decoder design does not.