The Dirichlet Process prior has been recently gaining popularity in Statistics and Economics as a useful tool for nonparametric density modeling. In particular, Dirichlet Process Mixture models (DPM) have been utilized in various settings involving unobserved heterogeneity. Nonetheless, the DPM has been rarely applied jointly in more than one dimension. One of the key reasons is a sharp decrease of acceptance probability of its individual mixture components and hence deterioration of mixing properties with each added dimension when using multivariate densities as the building blocks of the DPM. We propose a method for high-dimensional application of the DPM via first modeling nonparametrically individual marginal densities and then linking these into the joint density using a copula function. Preliminary output shows considerable promise of the proposed factorization method in breaking the DPM curse of dimensionality.