  We calculate the bounds which could be placed on scalar-tensor theories of
gravity of the Jordan, Fierz, Brans and Dicke type by measurements of
gravitational waveforms from neutron stars (NS) spiralling into massive black
holes (MBH) using LISA, the proposed space laser interferometric observatory.
Such observations may yield significantly more stringent bounds on the
Brans-Dicke coupling parameter \omega than are achievable from solar system or
binary pulsar measurements. For NS-MBH inspirals, dipole gravitational
radiation modifies the inspiral and generates an additional contribution to the
phase evolution of the emitted gravitational waveform. Bounds on \omega can
therefore be found by using the technique of matched filtering. We compute the
Fisher information matrix for a waveform accurate to second post-Newtonian
order, including the effect of dipole radiation, filtered using a currently
modeled noise curve for LISA, and determine the bounds on \omega for several
different NS-MBH canonical systems. For example, observations of a 1.4 solar
mass NS inspiralling to a 1000 solar mass MBH with a signal-to-noise ratio of
10 could yield a bound of \omega > 240,000, substantially greater than the
current experimental bound of \omega > 3000.
