Dielectric measurements (10(-2)-10(9) Hz) on plastically crystalline cyanocyclohexane reveal a glass transition where the rotational dynamics freezes at a vitrification temperature T-g=134 K. A full line-shape analysis of the dielectric loss spectra, which include a pronounced secondary relaxation contribution (beta process) in addition to the main relaxation, is performed. We show that the rotational dynamics in cyanocyclohexane is very similar to that of supercooled liquids. In particular the secondary process of cyanocyclohexane exhibits the features characteristic of the Johari-Goldstein beta relaxation known from structural glass formers.