Previously, dynamic-programming-based DNA sequence aligners were mostly implemented with a penalty function of the one-piece affine gap model. When aligning sequences with longer gaps, the two-piece affine gap model provides better results at the cost of memory usage, which becomes an issue especially for aligners with memory-hungry traceback capabilities. In this paper, we design a memory-efficient scheme for traceback recording with the two-piece penalty scoring, so that the aligner can be realized on an ASIC. Our design is implemented using TSMC 40nm technology, and the proposed aligner can speed up pairwise alignment by 71X when compared to the CPU approach.