In this thesis, we address the problem of service function chaining in a network. Currently, problems of chaining services in a network (i.e. service function chaining) can be broadly categorised into middlebox placement in a network and packet steering through middleboxes. In this work, we present a packet steering approach - One Pass Packet Steering (OPPS) - for use in multi-subscriber environments, with the aim that subscribers having similar policy chain composition should experience the same network performance. We develop and show algorithms with a proof of concept implementation using emulations performed with Mininet. We identify challenges and examine how OPPS could benefit from the Software Defined Data Center architecture to overcome these challenges. Our results show that, given a fixed topology and different sets of policy chains containing the same middleboxes, the end-to-end delay and throughput performance of subscribers using similar policy chains remains approximately the same. Also, we show how OPPS can use a smaller number of middleboxes and yet, achieve the same hop count as that of a reference model described in a previous work as ideal, without violating the subscribers' policy chains.