  Scalar-tensor theories (STTs) are a widely studied alternative to General
Relativity (GR) in which gravity is endowed with an additional scalar degree of
freedom. Although severely constrained by solar system and pulsar timing
experiments, there remains a large set of STTs which are consistent with all
present day observations. In this paper, we investigate the possibility of
probing a yet unconstrained region of the parameter space of STTs based on the
fact that stability properties of highly compact neutron stars in these
theories may radically differ from those in GR.
