We present spectroscopic abundance analyses of three main-sequence B stars in the young Large Magellanic Cloud cluster NGC 2004. All three targets have projected rotational velocities around 130 km/s. Techniques are presented that allow the derivation of stellar parameters and chemical abundances in spite of these high vsini values. Together with previous analyses of stars in this cluster, we find no evidence among the main-sequence stars for effects due to rotational mixing up to vsini~130 km/s. Unless the equatorial rotational velocities are significantly larger than the vsini values, this finding is probably in line with theoretical expectations. NGC 2004/B30, a star of uncertain evolutionary status located in the blue Hertzsprung gap, clearly shows signs of mixing in its atmosphere. To verify the effects due to rotational mixing will therefore require homogeneous analysis of statistically significant samples of low-metallicity main-sequence B stars over a wide range of rotational velocities.