  The historic first detection of the binary neutron star merger GW170817 by
the LIGO-Virgo collaboration has set a limit on the gravitational deformability
of neutron stars. In contrast, radio observations of PSR J0740+6620 find a very
massive neutron star. Tension between the small deformability and the large
maximum mass may suggest that the pressure rises rapidly with density and thus
the speed of sound in dense matter is likely a large fraction of the speed of
light. We use these observations and simple constant sound-speed model
equations of state to set a lower bound on the maximum speed of sound in
neutron stars. If the tidal deformability of a 1.4$M_\odot$ neutron star is
less than 600, as is suggested by subsequent analyses of GW170817, we find that
the sound speed in the cores of neutron stars is likely larger than the
conformal limit of $c/\sqrt{3}$. Implications of this for our understanding of
both hadronic and quark-gluon descriptions of dense matter are discussed.
