Corporate social responsibility (CSR) has been attracting increasing attention. This paper investigates the implications of CSR upon a two-period manufacturer–retailer supply chain with cost learning effects which have been widely observed in different industries. Two scenarios are under consideration: the retailer exhibits CSR in one and the manufacturer does in the other. The analytical results demonstrate that compared with no CSR, the implementation of CSR generates higher pure profit for the entire chain. In contrast to the scenario where the manufacturer shows CSR, in the scenario where the retailer exhibits CSR, the manufacturer charges higher wholesale prices while the retailer charges lower retail prices, resulting in a higher chain-wide profit. Moreover, two-part tariff contracts are designed to coordinate the socially responsible supply chains. When coordinated, if the retailer exhibits CSR the wholesale prices are equal to the realized production cost which results from cost learning effects, while the wholesale prices are lower than the realized production cost if the manufacturer shows CSR. Interestingly, cost learning effects impair the pure profit of the coordinated supply chain when the effect of CSR is sufficiently high.