  We present a search for Trojan companions to 25 transiting exoplanets. We use
the technique of Ford & Gaudi, in which a difference is sought between the
observed transit time and the transit time that is calculated by fitting a
two-body Keplerian orbit to the radial-velocity data. This technique is
sensitive to the imbalance of mass at the L4/L5 points of the planet-star
orbit. No companions were detected above 2\sigma confidence. The median 2\sigma
upper limit is 56 M_\earth, and the most constraining limit is 2.8 M_\earth for
the case of GJ 436. A similar survey using forthcoming data from the Kepler
satellite mission, along with the radial-velocity data that will be needed to
confirm transit candidates, will be sensitive to 10-50 M_\earth Trojan
companions in the habitable zones of their parent stars. As a by-product of
this study, we present empirical constraints on the eccentricities of the
planetary orbits, including those which have previously been assumed to be
circular. The limits on eccentricity are of interest for investigations of
tidal circularization and for bounding possible systematic errors in the
measured planetary radii and the predicted times of secondary eclipses.
