In this paper we develop a conditional likelihood based approach for estimating the equilibrium price and shares in markets with differentiated products and oligopoly supply. We model market demand using a discrete choice model with random coefficients and random utility. For most applications the likelihood function of equilibrium prices and shares is intractable and cannot be directly analyzed. To overcome this, we develop a Markov Chain Monte Carlo simulation strategy to estimate parameters and distributions based. To illustrate our methodology, we generate a dataset of prices and quantities simulated from a differentiated goods oligopoly across a number of markets. We apply our methodology to this dataset to demonstrate its attractive features as well as its accuracy and validity.