The popular DYNARE software package, which has proved useful for small- and medium-scale models is, however, not capable of handling such models, thus inhibiting the formulation and estimation of more realistic DSGE models. A primary goal of this paper is to introduce a user-friendly MATLAB software program designed to reliably estimate high-dimensional DSGE models. It simulates the posterior distribution by the tailored random block Metropolis-Hastings (TaRB-MH) algorithm of Chib and Ramamurthy (2010), calculates the marginal likelihood by the method of Chib (1995) and Chib and Jeliazkov (2001), and includes various post-estimation tools that are important for policy analysis, for example, functions for conducting impulse response and variance decomposition analyses, and point and density forecasts. Another goal is to provide pointers on the fitting of these DSGE models. An extended version of the new Keynesian model of Leeper, Traum and Walker (2017) that has 51 parameters, 21 endogenous variables, 8 exogenous shocks, 8 observables, and 1,494 non-Gaussian and nonlinear latent variables is considered in detail.