Service Function Chains (SFCs) comprise a sequence of Network Functions (NFs) that are typically traversed in-order by data flows. Consequently, SFC delay grows linearly with the length of the SFC. Yet, for highly latency sensitive applications, this delay may be unacceptable---particularly when the constituent NFs are virtualized, running on commodity servers. In this paper, we investigate how SFC latency may be reduced by exploiting opportunities for parallel packet processing across NFs. We propose ParaBox, a novel hybrid packet processing architecture that, when possible, dynamically distributes packets to VNFs in parallel and merges their outputs intelligently to ensure the preservation of correct sequential processing semantics. To demonstrate the feasibility of our approach, we implement a ParaBox prototype on top of the DPDK-enabled Berkeley Extensible Software Switch. Our preliminary experiment results show that ParaBox can not only significantly reduce the service chaining latency, but also improve throughput.