Numerical studies of binary neutron star mergers incorporate a rich selection of physics, including general relativistic hydrodynamics and magnetohydrodynamics, nuclear physics, in particular neutrino physics, and BH formation. One ingredient that has been neglected so far, in contrast to binary black hole simulations, is the role of the neutron star spins, which influences the spin of the resulting BH, which in turn is important to model short gamma ray bursts. We present first numerical results for the merger of spinning binary neutron stars with a simplified equation of state. In particular, we adress the question how close the angular momentum of the final BH can get to the theoretical maximum.