We study a supply chain in which an original equipment manufacturer (OEM) outsources manufacturing functions to a contract manufacturer (CM) for cost saving. In addition to accepting the OEM’s order, the CM can develop self-branded products and enter the end-market. Because of the OEM’s well-known brand and long-term good reputation, we take the asymmetric customer loyalty into consideration - a fraction of customers are loyal customers (LCs) who only consider buying the product from the OEM, while other customers in the market are non-loyal customers (NCs) who might switch to purchasing the CM’s product because of the lower selling price. We explore whether the CM will enter the end-market and if so, what is the impact of the market entry on the OEM and the entire supply chain. Counterintuitively, we find that there will be no market entry when the CM is relatively strong, i.e., the CM is able to provide self-branded products with relatively high acceptance and the CM has a relatively large bargaining power. In addition, when the NC segment is an important profit source for the OEM, i.e., the NCs’ market size is relatively large and their willingness-to-pay is relatively high, the market entry will not occur, either. The OEM’s profit is always hurt by the CM’s market entry unless the OEM always only sells the product to the LCs, while the supply chain sometimes can get benefit. Through numerical simulations, we reveal the relationships between the profit change of different parties and the key parameters, such as the relative willingness-to-pay and market sizes of two types of customers, the CM’s bargaining power and the acceptance of the CM’s product, when the market entry becomes an available option for the CM. The impact of production cost difference on the market entry decision and profit changes is also analyzed in the extension when producing the OEM’s product is more costly for the CM than producing the self-branded product.