In direct sequence code division multiple access (DS-CDMA), variable rate transmission can be realized by simply changing the spreading factor SF for the given chip rate. In a frequency-selective fading channel, the transmission performance can be improved by using rake combining. However, when a very low SF is used for achieving a high transmission rate, error floor is produced due to insufficient suppression of inter-chip interference (ICI). In this paper, decision feedback chip-level maximum likelihood detection (DF-CMLD) is proposed that can suppress the ICI. An upper-bound for the conditional bit error rate (BER) is theoretically derived for the given spreading sequence and path gains. The theoretical average BER performance is numerically evaluated by Monte-Carlo numerical computation using the derived conditional BER. The numerical computation results are confirmed by computer simulation of DS-CDMA signal transmission with DF-CMLD.