In this paper, we present an extension of the Genoa artificial stock market GASM) (Raberto et al., 2001) that includes a limit order book as mechanism for price formation. At every time step an agent is chosen with uniform distribution to issue an order. The order can be a limit order or a market order. If the order is a limit order, it is stored in the book; if the order is a market order, a transaction occurs. Prices are formed at variable time steps, i.e., only when a market order is issued. We investigate how the new asynchronous trading mechanism affects the statistical properties of simulated prices. This computational experiment shows that the fat tails of the returns distribution can be recovered simply as a consequence of the limit order book without any additional assumption on agents' behavior.