  The nuclear symmetry energy plays a role in determining both the nuclear
properties of terrestrial matter as well as the astrophysical properties of
neutron stars. The first measurement of the neutron star tidal deformability,
from gravitational wave event GW170817, provides a new way of probing the
symmetry energy. In this work, we report on new constraints on the symmetry
energy from GW170817. We focus in particular on the low-order coefficients:
namely, the value of the symmetry energy at the nuclear saturation density,
S_0, and the slope of the symmetry energy, L_0. We find that the gravitational
wave data are relatively insensitive to S_0, but that they depend strongly on
L_0 and point to lower values of L_0 than have previously been reported, with a
peak likelihood near L_0 ~ 20 MeV. Finally, we use the inferred posteriors on
L_0 to derive new analytic constraints on higher-order nuclear terms.
