The emerging Network Function Virtualization (NFV) paradigm, coupled with the highly flexible and programmatic control of network devices offered by Software Defined Networking solutions, enables unprecedented levels of network virtualization that will definitely change the shape of future network architectures, where legacy telco central offices will be replaced by cloud data centers located at the edge. On the one hand, this software-centric evolution of telecommunications will allow network operators to take advantage of the increased flexibility and reduced deployment costs typical of cloud computing. On the other hand, it will pose a number of challenges in terms of virtual network performance and customer isolation. This paper intends to provide some insights on how an open-source cloud computing platform such as OpenStack implements multitenant network virtualization and how it can be used to deploy NFV, focusing in particular on packet forwarding performance issues. To this purpose, a set of experiments is presented that refer to a number of scenarios inspired by the cloud computing and NFV paradigms, considering both single tenant and multitenant scenarios. From the results of the evaluation it is possible to highlight potentials and limitations of running NFV on OpenStack.