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With the emergence of network softwarization trend, traditional networking services offered by Internet providers are expected to evolve by fully leveraging new recent technologies like network function virtualization and software defined networking. In this paper, we investigate offering Service Function Chains as a Service (SFCaaS) in NFV Environments. We first describe the potential business model to offer such a service. We then conduct a detailed study of the costs of virtual machine instances offered by Amazon EC2 with respect to the location, instance size, and performance in order to guide service chain provisioning and resource allocation. Afterwards, we address the resource allocation problem for service chain functions from the SFC provider's perspective while leveraging the performed cost study. We hence formulate the problem as an Integer Linear Program (ILP) aiming at reducing the SFC provider's operational costs of virtual machine instances and links as well as the synchronization costs among the instances. We also propose a new heuristic algorithm to solve the mapping problem with the same aforementioned goals taking into account the conducted study of the costs of Amazon EC2 instances. We show through extensive simulations that the proposed heuristic significantly reduce operational costs compared to a Baseline algorithm inspired by the existing literature.