  In the presence of a perpendicular magnetic field, ABC-stacked trilayer
graphene's chiral band structure supports a 12-fold degenerate N=0 Landau level
(LL). Along with the valley and spin degrees of freedom, the zeroth LL contains
additional quantum numbers associated with the LL orbital index $% n=0,1,2$.
Remote inter-layer hopping terms and external potential difference $\Delta_{B}$
between the layers lead to LL splitting by introducing a gap $% \Delta_{LL}$
between the degenerate zero-energy triplet LL orbitals. Assuming that the spin
and valley degrees of freedom are frozen, we study the phase diagram of this
system resulting from competition of the single particle LL splitting and
Coulomb interactions within the Hartree-Fock approximation at integer filling
factors. Above a critical value $\Delta_{LL}^{c}$ of the external potential
difference i,e, for $|\Delta_{LL}| >\Delta_{LL}^{c}$, the ground state is a
uniform quantum Hall state where the electrons occupy the lowest unoccupied LL
orbital index. For $|\Delta_{LL}| <\Delta_{LL}^{c}$ (which corresponds to large
positive or negative values of $\Delta_{B}$) the uniform QH state is unstable
to the formation of a crystal state at integer filling factors. This phase
transition should be characterized by a Hall plateau transition as a function
of $\Delta_{LL}$ at a fixed filling factor. We also study the properties of
this crystal state and discuss its experimental detection.
