  The chiral glass behaviour of the nearest-neighbour random-bond XY spin glass
in four dimensions is studied by Monte Carlo simulations. A chiral glass
transition at $T_{cg}=0.90\pm 0.05$ is found by a finite-size scaling analysis
of the results. The associated chiral correlation-length exponent is estimated
to be $\nu_{cg}=0.6\pm 0.1$ and $\eta_{cg}\sim 0.25$. The values for the chiral
critical temperature and the exponents are very similar to those reported
recently for the spin glass transition in this model.
  The results strongly suggest a simultaneous ordering of spin and chirality in
four dimensions.
