  Scalar-tensor theories are among the simplest extensions of general
relativity. In theories with light scalars, deviations from Einstein's theory
of gravity are determined by the scalar mass m_s and by a Brans-Dicke-like
coupling parameter \omega_{BD}. We show that gravitational-wave observations of
nonspinning neutron star-black hole binary inspirals can be used to set lower
bounds on \omega_{BD} and upper bounds on the combination
m_s/\sqrt{\omega_{BD}}$. We estimate via a Fisher matrix analysis that
individual observations with signal-to-noise ratio \rho would yield
(m_s/\sqrt{\omega_{BD}})(\rho/10)<10^{-15}, 10^{-16} and 10^{-19} eV for
Advanced LIGO, ET and eLISA, respectively. A statistical combination of
multiple observations may further improve these bounds.
