  We present initial results from a new high-contrast imaging program dedicated
to stars that exhibit long-term Doppler radial velocity accelerations (or
"trends"). The goal of the TRENDS (TaRgetting bENchmark-objects with Doppler
Spectroscopy and) imaging survey is to directly detect and study the companions
responsible for accelerating their host star. In this first paper of the
series, we report the discovery of low-mass stellar companions orbiting HD
53665, HD 68017, and HD 71881 using NIRC2 adaptive optics (AO) observations at
Keck. Follow-up imaging demonstrates association through common proper-motion.
These co-moving companions have red colors with estimated spectral-types of
K7--M0, M5, and M3--M4 respectively. We determine a firm lower-limit to their
mass from Doppler and astrometric measurements. In the near future, it will be
possible to construct three-dimensional orbits and calculate the dynamical mass
of HD 68017 B and possibly HD 71881 B. We already detect astrometric orbital
motion of HD 68017 B, which has a projected separation of 13.0 AU. Each
companion is amenable to AO-assisted direct spectroscopy. Further, each
companion orbits a solar-type star, making it possible to infer metallicity and
age from the primary. Such benchmark objects are essential for testing
theoretical models of cool dwarf atmospheres.
