Goodwin’s “A Growth Cycle” [1967] represents a milestone in the non-linear modeling of economic dynamics. In terms of the two variables “wage share” and “employment rate” and on the basis of few simple assumptions, the Goodwin Model (GM) is formulated exactly as the well-known Lotka-Volterra system, with all the limits of such system, in particular the lacking of structural stability. A number of extensions have been proposed with the aim to make the model more robust. We propose a new extension that: a) removes the limiting hypothesis of “Harrod-neutral” technical progress: b) on the line of Lotka-Volterra models with adaptation, introduces the concept of “memory”, which certainly plays a relevant role in the dynamics of economic systems. As a consequence an additional equation appears, the validity of the model is substantially extended and a rich phenomenology is obtained, in particular transition to chaotic behavior via period-doubling bifurcations.