This paper presents a dynamic stochastic general equilibrium (DSGE) model for a small open economy fitted to Icelandic data. The model has been developed at the Central Bank of Iceland as a tool for policy analysis and forecasting purposes in support of inflation targeting. As the existing macroeconometric model at the Central Bank, the model is a dynamic quarterly model. But it differs by being fully founded on well-defined microeconomic decision problems of agents in the economy. This allows for a structural interpretation of shocks to the economy. The model features endogenous capital accumulation subject to investment adjustment costs, variable capacity utilisation, habit formation in consumption, monopolistic competition in goods and labour markets, as well as sticky prices and wages. The home economy engages freely in international trade, while international financial intermediation is subject to endogenous costs. Monetary policy is conducted by an inflation targeting central bank. The model is fitted to Icelandic data for the sample period 1991-2005 through a combination of calibration and formal Bayesian estimation. The paper presents the estimation results, and it discusses the model's properties. Finally, first applications are shown to illustrate the model's potential in guiding monetary policy.