  We search for periodic variations in the radial velocity of the young Herbig
star HD 135344B with the aim to determine a rotation period. We analyzed 44
high-resolution optical spectra taken over a time range of 151 days. The
spectra were acquired with FEROS at the 2.2m MPG/ESO telescope in La Silla. The
stellar parameters of HD 135344B are determined by fitting synthetic spectra to
the stellar spectrum. In order to obtain radial velocity measurements, the
stellar spectra have been cross-correlated with a theoretical template computed
from determined stellar parameters. We report the first direct measurement of
the rotation period of a Herbig star from radial-velocity measurements. The
rotation period is found to be 0.16 d (3.9 hr), which makes HD 135344B a rapid
rotator at or close to its break-up velocity. The rapid rotation could explain
some of the properties of the circumstellar environment of HD 135344B such as
the presence of an inner disk with properties (composition, inclination), that
are significantly different from the outer disk.
