  The direct detection of gravitational waves (GWs) is an invaluable new tool
to probe gravity and the nature of cosmic acceleration. A large class of
scalar-tensor theories predict that GWs propagate with velocity different than
the speed of light, a difference that can be $\mathcal{O}(1)$ for many models
of dark energy. We determine the conditions behind the anomalous GW speed,
namely that the scalar field spontaneously breaks Lorentz invariance and
couples to the metric perturbations via the Weyl tensor. If these conditions
are realized in nature, the delay between GW and electromagnetic (EM) signals
from distant events will run beyond human timescales, making it impossible to
measure the speed of GWs using neutron star mergers or other violent events. We
present a robust strategy to exclude or confirm an anomalous speed of GWs using
eclipsing binary systems, whose EM phase can be exquisitely determined. he
white dwarf binary J0651+2844 is a known example of such system that can be
used to probe deviations in the GW speed as small as $c_g/c-1\gtrsim 2\cdot
10^{-12}$ when LISA comes online. This test will either eliminate many
contender models for cosmic acceleration or wreck a fundamental pillar of
general relativity.
