In this paper, we focus on n-player strategic chance-constrained games where the payoff of each player follows either Cauchy or normal distributions. We prove the equivalence between a Nash equilibrium problem and a variational inequality problem. We reformulate the latter as a nonlinear complementarity problem (NCP) through the Karush-Kuhn-Tucker (KKT) conditions. Then, we prove the existence of the Nash equilibrium via Brouwer's fixed-point theorem. In order to show the efficiency of our approach, we perform numerical experiments on a set of randomly generated instances.