  We report on 1.7 and 5.0 GHz observations of the z=3.087 radio galaxy B3
J2330+3927, using the Very Long Baseline Array (VLBA), and archival 1.4 and 8.4
GHz Very Large Array (VLA) data. Our VLBA data identify a compact, flat
spectrum (\alpha_{1.7 GHz}^{5 GHz} = -0.2 +/- 0.1; S_\nu ~ \nu^\alpha) radio
component as the core. The VLA images show that the fraction of core emission
is very large (f_c \approx 0.5 at 8.4 GHz), and reveal a previously undetected,
very faint counterjet, implying a radio lobe flux density ratio R >= 11 and a
radio lobe distance ratio Q \approx 1.9. Those values are much more common in
quasars than in radio galaxies, but the optical/near-IR spectra show a clear
type II AGN for B3 J2330+3927, confirming that it is indeed a radio galaxy.
Unlike all other radio galaxies, the bright Ly-\alpha emitting gas is located
towards the furthest radio arm. We argue against environmental and relativistic
beaming effects being the cause of the observed asymmetry, and suggest this
source has intrinsically asymmetric radio jets. If this is the case, B3
J2330+3927 is the first example of such a source at high redshift, and seems to
be difficult to reconcile with the unified model, which explains the
differences between quasars and radio galaxies as being due to orientation
effects.
