Software-defined networking (SDN) and network function virtualization (NFV) processed in multi-access edge computing (MEC) cloud systems have been proposed as critical paradigms for achieving the low latency requirements of the tactile Internet. While virtual network functions (VNFs) allow greater flexibility compared to hardware-based solutions, the VNF abstraction also introduces additional packet processing delays. In this paper, we investigate the practical feasibility of NFV with respect to the tactile Internet latency requirements. We develop, implement, and evaluate Chain-based Low latency VNF ImplemeNtation (CALVIN), a low-latency management framework for distributed Service Function Chains (SFCs). CALVIN classifies VNFs into elementary, basic, and advanced VNFs; moreover, CALVIN implements elementary and basic VNFs in the kernel space, while the advanced VNFs are implemented in the user space. Throughout, CALVIN employs a distributed mapping with one VNF per Virtual Machine (VM) in a MEC system. Furthermore, CALVIN avoids the metadata structure processing and batch processing of packets in the conventional Linux networking stack so as to achieve short per-packet latencies. Our rigorous measurements on off-the-shelf conventional networking and computing hardware demonstrate that CALVIN achieves round-trip times from a MEC ingress point via two elementary forwarding VNFs (one in kernel space and one in user space) and a MEC server to a MEC egress point on the order of 0.32 ms. Our measurements also indicate that MEC network coding and encryption are feasible for small 256 byte packets with an MEC latency budget of 0.35 ms; whereas, large 1400 byte packets can complete the network coding, but not the encryption within the 0.35 ms.