The Cloud phenomenon is quickly growing towards becoming the de facto standard of Internet Computing, storage and hosting both in industry and academia. The large scalability possibilities offered by Cloud platforms can be harnessed not only for services and applications hosting but also as a raw on-demand computing resource. This paper proposes the use of a Cloud system as a raw computational on-demand resource for a Grid middleware. We illustrate a proof of concept by considering the DIET-Solve Grid middleware and the EUCALYPTUS open-source Cloud platform.