Answer
It might, in which case the gene would be a character defining chordates above the lancelets as a clade. However, it is also possible that the gene could have been in the common ancestor and then lost in the lancelet branch of the chordates.
Work Step by Step
The key here is to see that a feature could be lost on one branch of a phylogenetic tree or never present before a certain point. There is not enough information in the question to distinguish between these two.