It is increasingly common to outsource network functions (NFs) to the cloud. However, no cloud providers offer NFs-as-a-Service (NFaaS) that allows users to run custom NFs. Our work addresses how a cloud provider can offer NFaaS. We use the emerging serverless computing paradigm as it has the right building blocks - usage-based billing, convenient event-driven programming model and automatic compute elasticity. Towards this end, we identify two core limitations of existing serverless platforms to support demanding stateful NFs - coupling of the billing and work assignment granularities, and state sharing via an external store. We develop a novel NFaaS framework, SNF, that overcomes these issues using two ideas. SNF allocates work at the granularity of flowlets observed in network traffic, whereas billing and programming occur on the basis of packets. SNF embellishes serverless platforms with ephemeral state that lasts for the duration of the flowlet and supports high performance state operations between compute units in a peer-to-peer manner. We present algorithms for work allocation and state maintenance, and demonstrate that our SNF prototype dynamically adapts compute resources for various stateful NFs based on traffic demand at very fine time scales, with minimal overheads.