We study a decentralized supply chain where only delayed market demand information is available for making replenishment decisions. The impact of this delay is quantified in a serially linked two-level supply chain where each player exploits the order-up-to replenishment policy. The market demand is assumed to be a first-order autoregressive process. It is shown that the first level of the supply chain benefits from shorter time delays; however, the benefit for the second level is quite minor at best and can sometimes even be (counter-intuitively) detrimental. We conclude that the second level does not have a strong incentive to reduce the time delays in the shared market demand information.