We propose that the rate of creation and failure of start-up firms can be modelled as a search and matching process, following labor market matching models. Setting out an endogenous growth model with entrepreneurship we derive a Entrepreneurship Beveridge Curve, through which we illustrate that entrepreneurial start-ups are the outcome of the efficiency with which entrepreneurial abilities are matched with business opportunities. The Entrepreneurship Beveridge Curve is a potentially useful analytical tool to add to the formalization of the economics of entrepreneurship, and we mention a number of extentions and applications.