Developed in the middle sixties, Šil’nikov Theory was first applied to the analysis of economic dynamics by H. W. Lorenz in the early nineties, His contribution created some optimism, among economists, about the possibility of employing Šil’nikov’s results to investigate complex dynamics in continuous-time economic models. In spite of this, after almost a decade, there are still no other contributions in the economis dynamic theory which considers chaotic motions arising from the set of conditions underlying the so called “Šil’nikov scenario”. This chapter fills the gap, providing a simple Keynesian growth model with endogenous technical progress and rational expectations which exhibits Šil’nikov dynamics.