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Credential chains are needed in trusted peer-to-peer (P2P) applications, where trust delegation must be established between each pair of peers at specific role level. Role-based trust is refined from the coarse-grained trust model used in most P2P reputation systems. This paper offers a novel heuristic-weighting approach to selecting the most likely path to construct a role-based trust chain. We apply history-sensitive heuristics to measure the path complexity and assess the chaining efficiency. We discover successive edges of a trust chain, adaptively, to match with the demands from various P2P applications. New heuristic chaining algorithms are developed for backward, forward, and bi-directional discovery of trust chains. Our heuristic chain discovery scheme shortens the search time, reduces the memory requirement, and enhances the chaining accuracy in scalable P2P networks. Consider a trust graph over N credentials and M distinct role nodes. Our heuristic trust-chain discovery algorithms require O(N2 logN) search time and O(M) memory space, if the secondary heuristics are generated off-line in advance. These are improved from O(N3) search time and O(NM) space required in non-heuristic discovery algorithms by Li, Winsborough, and Mitchell (2003). Our analytical results are verified by extensive simulation experiments over typical classes of role-based trust graphs.