  We analyze the dissipative conductance of the zero-plateau quantum Hall state
appearing in undoped graphene in strong magnetic fields. Charge transport in
this state is assumed to be carried by a magnetic domain wall, which forms by
hybridization of two counter--propagating edge states of opposing spin due to
interactions. The resulting non--chiral edge mode is a Luttinger liquid of
parameter K, which enters a gapped, perfectly conducting state below a critical
value K_c\approx 1/2. Backscattering in this system involves spin flip, so that
interaction with localized magnetic moments generates a finite resistivity
R_{xx} via a "chiral Kondo effect". At finite temperatures T, R_{xx}(T)
exhibits a crossover from metallic to insulating behavior as K is tuned across
a threshold K_{MI}. For T->0, R_{xx} in the intermediate regime K_{MI}<K<K_c is
finite, but diverges as K approaches K_c. This model provides a natural
interpretation of recent experiments.
