  We study the superfluidity of a spin-orbit coupled Bose-Einstein condensate
(BEC) by computing its Bogoliubov excitations, which are found to consist of
two branches: one is gapless and phonon-like at long wavelength; the other is
typically gapped. These excitations imply a superfluidity that has two new
features: ({\it i}) due to the absence of the Galilean invariance, one can no
longer define the critical velocity of superfluidity independent of the
reference frame; ({\it ii}) the superfluidity depends not only on whether the
speed of the BEC exceeds a critical value, but also on {\it cross helicity}
that is defined as the direction of the cross product of the spin and the
kinetic momentum of the BEC.
