An one-way hash chain generated by the iterative use of a one-way hash function on a secret value has recently been widely employed to develop many practical cryptographic solutions, especially electronic micropayment schemes. In this paper, we propose a new concept called a weighted one-way hash chain. We then proceed to use the new concept to improve in a significant way the performance of micropayment schemes. We also show that the proposed technique is especially useful in implementing micropayment on a resource restrained computing device such as a hand-held computer.