  The {\em metric dimension} of a graph $\Gamma$ is the least number of
vertices in a set with the property that the list of distances from any vertex
to those in the set uniquely identifies that vertex. We consider the Grassmann
graph $G_q(n,k)$ (whose vertices are the $k$-subspaces of $\mathbb{F}_q^n$, and
are adjacent if they intersect in a $(k-1)$-subspace) for $k\geq 2$, and find a
constructive upper bound on its metric dimension. Our bound is equal to the
number of 1-dimensional subspaces of $\mathbb{F}_q^n$.
