We derive a time-efficient method for building a multiple alignment consisting of a highest-scoring chain of "blocks," i.e., short gap-free alignments. Besides executing faster than a general-purpose multiple-alignment program, the method may be particularly appropriate when discovery of blocks meeting a certain criterion is the main reason for aligning the sequences. Utility of the method is illustrated by locating a chain of "phylogenetic footprints" (specifically, exact matches of length 6 or more) in the 5'-flanking regions of six mammalian epsilon-globin genes.