We obtain a new weak Hilton-Milner type result for intersecting families of k-spaces in F 2k q , which improves several known results. In particular the chromatic number of the q-Kneser graph qK n:k was previously known for n > 2k (except for n = 2k + 1 and q = 2) or k < q log q − q. Our result determines the chromatic number of qK 2k:k for q ≥ 5, so that the only remaining open cases are (n, k) = (2k, k) with q ∈ {2, 3, 4} and (n, k) = (2k + 1, k) with q = 2.