  We study the electronic instabilities of near 1/4 electron doped graphene
using the functional renormalization group (FRG) and variational Monte-Carlo
method. A modified FRG implementation is utilized to improve the treatment of
the von Hove singularity. At 1/4 doping the system is a chiral spin density
wave state exhibiting the anomalous quantized Hall effect, or equivalently a
Chern insulator. When the doping deviates from 1/4, the $d_{x^2-y^2}+i d_{xy}$
Cooper pairing becomes the leading instability. Our results suggest near 1/4
electron or hole doped graphene is a fertile playground for the search of Chern
insulators and superconductors.
