We present the first space and time optimal parallel algorithm for the pairwise sequence alignment problem, a fundamental problem in computational biology. This problem can be solved sequentially in O(mn) time and O(m +n) space, where m and n are the lengths of the sequences to be aligned. The fastest known parallel space-optimal algorithm for pairwise sequence alignment takes optimal O (\frac{{m + n}} {p}) space but supboptimal O (\frac{{(m + n)^2 }} {p}) time, where p is the number of processors. On the other hand, the most space economical time-optimal parallel algorithm takes O (\frac{{mn}} {p}) time but O (m + \frac{n} {p}) space. We close this gap by presenting an algorithm that achieves both time and space optimality, i.e. requires only O (\frac{{m + n}} {p}) space and O (\frac{{mn}} {p}) time. We also present an experimental evaluation of the proposed algorithm on an IBM xSeries cluster.