In service function chaining (SFC), end-To-end traffic flows are classified and processed by an ordered set of service functions (SFs). When SF in the chain fails, the corresponding traffic flows cannot be processed further to reach the destination until the failed SF recovers. To cope with the SF failure, failover mechanisms to instantly recover such failed SFs are mandatory. In this paper, we propose a distributed SF failover mechanism where a distributed failover agent (DFA) located along with each SF instance conducts failure detection/recovery of the failed SF. By doing so, the failed SFs can be recovered without interventions of the centralized SFC controller. Simulation results are shown that the distributed SF failover mechanism significantly reduces the average failover time by 56-76% compared to the centralized SF failover mechanism.