This paper describes a low complexity equalizer for the ISI channel, which approximates a maximum likelihood sequence estimator (MLSE). Our equalizer is an extension of the SLIC demodulator for the MIMO channel, presented recently. SLIC stands for serial localization with indecision and color suppression. The main features of the SLIC equalizer are: 1) a serial structure, where the search for the eventual solution is incrementally localized in each stage; 2) each stage includes a MLSE operating on centroids as a proxy for true constellation symbols; 3) centroids represent subsets of true symbols, and the subsets overlap by design. The overlap enables the indecision feature, which is desirable because it prevents an early stage from making an irreparable erroneous decision. The use of centroids creates an intentional residual signal, which is left to a later stage to resolve, and is suppressed as a colored noise in the current stage. We present performance results with different subset designs for 16 and 64QAM. Overall, we show that the SLIC equalizer is an attractive tradeoff of complexity and performance for the ISI channel.