  We study superconductivity on the honeycomb lattice close to the Mott state
at half-filling. Due to the sixfold lattice symmetry and disjoint Fermi
surfaces at opposite momenta, we show that several different fully gapped
superconducting states naturally exist on the honeycomb lattice, of which the
chiral $d+id'$-wave state has previously been shown to appear when
superconductivity appears close to the Mott state. Using renormalized
mean-field theory to study the t-J model and quantum Monte Carlo calculations
of the Hubbard-U model we show that the $d+id'$-wave state is the favored
superconducting state for a wide range of on-site repulsion U, from the
intermediate to the strong coupling regime. We also investigate the possibility
of a mixed chirality d-wave state, where the overall chirality cancels. We find
that a state with $d+id'$-wave symmetry in one valley but $d-id'$-wave symmetry
in the other valley is not possible in the t-J model without reducing the
translational symmetry, due to the zero-momentum and spin-singlet nature of the
superconducting order parameter. Moreover, any extended unit cells result
either in disjoint Dirac points, which cannot harbor this mixed chirality
state, or the two valleys are degenerate at the zone center, where valley
hybridization prevents different superconducting condensates. We also
investigate extended unit cells where the overall chirality cancels in real
space. For supercells containing up to eight sites, including the Kekul\'{e}
distortion, we find no energetically favorable d-wave solution with an overall
zero chirality within the restriction of the t-J model.
