  An overwhelming majority of galactic spiral arms trail with respect to the
rotation of the galaxy, though a small sample of leading spiral arms has been
observed. The formation of these leading spirals is not well understood. Here
we show, using collisionless $N$-body simulations, that a barred disc galaxy in
a retrograde dark matter halo can produce long-lived ($\sim3$ Gyr) leading
spiral arms. Due to the strong resonant coupling of the disc to the halo, the
bar slows rapidly and spiral perturbations are forced ahead of the bar. We
predict that such a system, if observed, will also host a dark matter wake
oriented perpendicular to the stellar bar. More generally, we propose that any
mechanism that rapidly decelerates the stellar bar will allow leading spiral
arms to flourish.
