This paper investigates the optimal timing and level of wholesale and retail prices set in multi-channel supply chains, where a manufacturer produces and sells products to retailers that compete to resell the products, by applying the framework of an observable delay game devised in noncooperative game theory. We assume that one manufacturer and two retailers, which constitute a two-echelon supply chain, can select not only the levels of wholesale and retail prices, respectively, but also the timing of pricing. Our analysis of a dynamic game composed of discrete periods provides two useful conclusions for operational decision support. First, the manufacturer must simultaneously set its wholesale prices for products that are sold to separate retailers at the same time. Second, in contrast to the simultaneous price setting by the manufacturer, the retailers must sequentially set respective retail prices at different times; thus, the retailers should stagger their timings for setting retail prices. We formally demonstrate that these timings of pricing decisions by the manufacturer and the retailers constitute a subgame perfect Nash equilibrium in the dynamic noncooperative game played by the three supply chain parties. Consequently, these conclusions can be used as practical guidelines for supply chain members choosing optimal timing of pricing.