  The standard explanation for large pulsar glitches involves transfer of
angular momentum from an internal superfluid component to the star's crust.
This model requires an instability to trigger the sudden unpinning of the
vortices by means of which the superfluid rotates. This Letter describes a new
instability that may play this role. The instability, which is associated with
the inertial r-modes of a superfluid neutron star, sets in once the rotational
lag in the system reaches a critical level. We demonstrate that our model is in
good agreement with observed glitch data, suggesting that the superfluid r-mode
instability may indeed be the mechanism that triggers large pulsar glitches.
