The emergence of Network Function Virtualization (NFV) enables flexible and agile service function chaining in a Software Defined Network (SDN). While this virtualization technology efficiently offers customization capability, it however comes with a cost of consuming precious TCAM resources. Due to this, the number of service chains that an SDN can support is limited by the flowtable size of a switch. To break this limitation, this paper presents CRT-Chain, a service chain forwarding protocol that requires only constant flowtable entries, regardless of the number of service chain requests. The core of CRT-Chain is an encoding mechanism that leverages Chinese Remainder Theorem (CRT) to compress the forwarding information into small labels. A switch does not need to insert forwarding rules for every service chain request, but only needs to conduct very simple modular arithmetic to extract the forwarding rules directly from CRT-Chain's labels attached in the header. We further incorporate prime reuse and path segmentation in CRT-Chain to reduce the header size and, hence, save bandwidth consumption. Our evaluation results show that, when a chain consists of no more than 5 functions, CRT-Chain actually generates a header smaller than the legacy 32-bit header defined in IETF. By enabling prime reuse and segmentation, CRT-Chain further reduces the total signaling overhead to a level lower than the conventional scheme, showing that CRT-Chain not only enables scalable flowtable-free chaining but also improves network efficiency.