  We use gravitational-wave observations of the binary neutron star merger
GW170817 to explore the tidal deformabilities and radii of neutron stars. We
perform Bayesian parameter estimation with the source location and distance
informed by electromagnetic observations. We also assume that the two stars
have the same equation of state; we demonstrate that for stars with masses
comparable to the component masses of GW170817, this is effectively implemented
by assuming that the stars' dimensionless tidal deformabilities are determined
by the binary's mass ratio $q$ by $\Lambda_1/\Lambda_2 = q^6$. We investigate
different choices of prior on the component masses of the neutron stars. We
find that the tidal deformability and 90$\%$ credible interval is
$\tilde{\Lambda}=222^{+420}_{-138}$ for a uniform component mass prior,
$\tilde{\Lambda}=245^{+453}_{-151}$ for a component mass prior informed by
radio observations of Galactic double neutron stars, and
$\tilde{\Lambda}=233^{+448}_{-144}$ for a component mass prior informed by
radio pulsars. We find a robust measurement of the common areal radius of the
neutron stars across all mass priors of $8.9 \le \hat{R} \le 13.2$ km, with a
mean value of $\langle \hat{R} \rangle = 10.8$ km. Our results are the first
measurement of tidal deformability with a physical constraint on the star's
equation of state and place the first lower bounds on the deformability and
areal radii of neutron stars using gravitational waves.
