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.Comment: Accepted for publication in Astronomy & Astrophysics, 9 pages, 12 figure
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