Network Function Virtualization (NFV) has proliferated the way network services are offered to the end users. Individual network functions are decoupled from expensive and dedicated middleboxes and are now provided as software-based virtualized entities called Virtualized Network Functions (VNFs). The multiple advantages that NFV introduces and the reduction of operational and capital expenses that are promised have greatly attracted the Enterprise and Service Providers to reap the benefits of adopting NFV in their product portfolio. However, one of the most important challenges is the efficient placement of multiple chained VNFs in a cloud-based managed service scenario. To this end, in this paper we propose a novel approach to facilitate the placement and deployment of chained VNFs in a network cloud infrastructure that can be extended using the Multi-Access Edge Computing (MEC) standard for accommodating mission critical and delay sensitive traffic. Our aim is to minimize the end-to-end communication delay while keeping the overall deployment cost to minimum. Results reveal that the proposed approach can significantly reduce the delay experienced, while satisfying Service Providers' goal of low deployment costs.