  We study a spin-1/2 SU(2) model on the honeycomb lattice with
nearest-neighbor antiferromagnetic exchange $J$ that favors N\'eel order, and
competing 6-spin interactions $Q$ which favor a valence bond solid (VBS) state
in which the bond-energies order at the "columnar" wavevector ${\mathbf K} =
(2\pi/3,-2\pi/3)$. We present quantum Monte-Carlo evidence for a direct
continuous quantum phase transition between N\'eel and VBS states, with
exponents and logarithmic violations of scaling consistent with those at
analogous deconfined critical points on the square lattice. Although this
strongly suggests a description in terms of deconfined criticality, the
measured three-fold anisotropy of the phase of the VBS order parameter shows
unusual near-marginal behaviour at the critical point.
