Communicative alignment refers to adaptation to one's communication partner. Temporal aspects of such alignment have been little explored. This article examines temporal aspects of lexical and syntactic alignment (i.e., tendencies to use the interlocutor's lexical items and syntactic structures) in task-oriented discourse. In particular, we investigate whether lexical and syntactic alignment increases throughout the discourse and whether alignment contributes to speedy task completion. We present data from a text-based chat game in which participants instructed each other on where to place objects in a grid. Our methodological approach allows calculating a robust baseline and revealed reliable lexical and syntactic alignment. However, only lexical alignment, but not syntactic alignment, was sensitive to temporal aspects in that only lexical alignment increased throughout the discourse and positively affected task completion time. We discuss how these results relate to the communicative task and mention implications for models of alignment.