  We have studied the ground states of two dimensional lattice model of Coulomb
Glass via Monte Carlo annealing. Our results show a possibility of existence of
a critical disorder (Wc) below which the system is in the charge ordered phase
and above it the system is in the disordered phase. We have used finite size
scaling to calculate Wc = 0.2413, the critical exponent of magnetization
{\beta} = 0 indicating discontinuity in magnetization and the critical exponent
of correlation length {\nu} = 1.0. The distribution of staggered magnetization
for different disorder strengths shows a three peak structure. We thus predict
that two dimensional Coulomb Glass shows a first order transition at T=0.
