  Using general-relativistic hydrodynamical simulations, we show that merging
binary neutron stars can form hypermassive neutrons stars that undergo the
one-arm spiral instability. We study the particular case of a dynamical capture
merger where the stars have a small spin, as may arise in globular clusters,
and focus on an equal-mass scenario where the spins are aligned with the
orbital angular momentum. We find that this instability develops when
post-merger fluid vortices lead to the generation of a toroidal remnant - a
configuration whose maximum density occurs in a ring around the center-of-mass
- with high vorticity along its rotation axis. The instability quickly
saturates on a timescale of $\sim 10$ ms, with the $m=1$ azimuthal density
multipole mode dominating over higher modes. The instability also leaves a
characteristic imprint on the post-merger gravitational wave signal that could
be detectable if the instability persists in long-lived remnants.
