  We present high-precision relative radial velocities of the very low-mass
star VB10 that were obtained over a time span of 0.61 yr as part of an ongoing
search for planets around stars at the end of the main sequence. The radial
velocities were measured from high-resolution near-infrared spectra obtained
using the CRIRES instrument on the VLT with an ammonia gas cell. The typical
internal precision of the measurements is 10 m/s. These data do not exhibit
significant variability and are essentially constant at a level consistent with
the measurement uncertainties. Therefore, we do not detect the radial velocity
variations of VB10 expected due to the presence of an orbiting giant planet
similar to that recently proposed by Pravdo and Shaklan based on apparent
astrometric perturbations. In addition, we do not confirm the ~1 km/s radial
velocity variability of the star tentatively detected by Zapatero Osorio and
colleagues with lower precision measurements. Our measurements rule out planets
with M_p > 3 M_Jup and the orbital period and inclination suggested by Pravdo
and Shaklan at better than 5 sigma confidence. We conclude that the planet
detection claimed by Pravdo and Shaklan is spurious on the basis of this
result. Although the outcome of this work is a non-detection, it illustrates
the potential of using ammonia cell radial velocities to detect planets around
very low-mass stars.
