  As proved by Kahn, the chromatic number and fractional chromatic number of a
line graph agree asymptotically. That is, for any line graph $G$ we have
$\chi(G) \leq (1+o(1))\chi_f(G)$. We extend this result to quasi-line graphs,
an important subclass of claw-free graphs. Furthermore we prove that we can
construct a colouring that achieves this bound in polynomial time, giving us an
asymptotic approximation algorithm for the chromatic number of quasi-line
graphs.
