  We introduce a new, powerful method to constrain properties of neutron stars
(NSs). We show that the total mass of GW170817 provides a reliable constraint
on the stellar radius if the merger did not result in a prompt collapse as
suggested by the interpretation of associated electromagnetic emission. The
radius R_1.6 of nonrotating NSs with a mass of 1.6 M_sun can be constrained to
be larger than 10.68_{-0.04}^{+0.15} km, and the radius R_max of the
nonrotating maximum mass configuration must be larger than 9.60_{-0.03}^{+0.14}
km. We point out that detections of future events will further improve these
constraints. Moreover, we show that a future event with a signature of a prompt
collapse of the merger remnant will establish even stronger constraints on the
NS radius from above and the maximum mass M_max of NSs from above. These
constraints are particularly robust because they only require a measurement of
the chirp mass and a distinction between prompt and delayed collapse of the
merger remnant, which may be inferred from the electromagnetic signal or even
from the presence/absence of a ringdown gravitational-wave (GW) signal. This
prospect strengthens the case of our novel method of constraining NS
properties, which is directly applicable to future GW events with accompanying
electromagnetic counterpart observations. We emphasize that this procedure is a
new way of constraining NS radii from GW detections independent of existing
efforts to infer radius information from the late inspiral phase or postmerger
oscillations, and it does not require particularly loud GW events.
