  The properties of neutron stars are determined by the nature of the matter
that they contain. These properties can be constrained by measurements of the
star's size. We obtain stringent constraints on neutron-star radii by combining
multimessenger observations of the binary neutron-star merger GW170817 with
nuclear theory that best accounts for density-dependent uncertainties in the
equation of state. We construct equations of state constrained by chiral
effective field theory and marginalize over these using the gravitational-wave
observations. Combining this with the electromagnetic observations of the
merger remnant that imply the presence of a short-lived hyper-massive neutron
star, we find that the radius of a $1.4\,\rm{M}_\odot$ neutron star is
$R_{1.4\,\mathrm{M}_\odot} = 11.0^{+0.9}_{-0.6}~{\rm km}$ (90% credible
interval). Using this constraint, we show that neutron stars are unlikely to be
disrupted in neutron-star black-hole mergers; subsequently, such events will
not produce observable electromagnetic emission.
