The chain range-join of k sets, S1, S2, …, Sk, is the set containing all tuples (s1, s2, …, sk) that satisfy e(1)i≤∣∣si−si+1∣∣≤e(2)i⁠, where sk∈ Sk,si∈Si,e(1)i≤e(2)i are fixed constants, 1 ≤ i ≤ k − 1. This paper presents an efficient parallel algorithm for computing the k-set chain range-join in hypercube computers. The proposed algorithm applies the technique of permutation-based range-join and works by joining data sets one by one along the chain. To compute the range-join of k sets S1, S2, …, Sk in a hypercube of p processors, p ≤ |Si| = ni and 1 ≤ i ≤ k, our algorithm requires only yO(∑ki=1nip) local memory at each processor, and has a time complexity at most O(((nk/p) + nk−1) log(nk/p)) in the best case when no element in St + 1 matches any element in St, for 1≤t≤k−1,O(kTsort+(k2/pΠki=1ni)) in the worst case when all elements in St + 1 match each element in St, where Tsort=O((K/P)Πki=2nilogΠki−2ni) when all elements in St + 1 are distinct, and Tsort=O((K/P)Πki=2ni) when all elements in St + 1 are equal. The general-case time complexity of the algorithm is also shown. The algorithm is implemented on a UNIX-based network using a simulator designed in C and its performance is fully evaluated through extensive testing.