In this paper, a family of copula functions called chi-square copula family is used for modeling the dependency structure of stationary and isotropic spatial random fields. The dependence structure of this copula is such that, it generalizes the Gaussian copula and flexible for modeling for high-dimensional random vectors and unlike Gaussian copula it allows for modeling of tail asymmetric dependence structures. Since the density function of chi-square copula in high dimension has computational complexity, therefore to estimate its parameters, a composite pairwise likelihood method is used in which only bivariate density functions are used. The purpose of this paper is to investigate the properties of the chi-square copula family, estimating its parameters with the composite pairwise likelihood and its application in spatial interpolation.