This paper gives an online algorithm for generating Jakobsson's fractal hash chains. Our new algorithm compliments Jakobsson's fractal hash chain algorithm for preimage traversal since his algorithm assumes the entire hash chain is precomputed and a particular list of Ceiling(log n) hash elements or pebbles are saved. Our online algorithm for hash chain traversal incrementally generates a hash chain of n hash elements without knowledge of n before it starts. For any n, our algorithm stores only the Ceiling(log n) pebbles which are precisely the inputs for Jakobsson's amortized hash chain preimage traversal algorithm. This compact representation is useful to generate, traverse, and store a number of large digital hash chains on a small and constrained device. We also give an application using both Jakobsson's and our new algorithm applied to digital chains of custody for validating dynamically changing forensics data.