We advocate the notion of service overlay network (SON) as an effective means to address some of the issues, in particular end-to-end QoS, plaguing the current Internet, and to facilitate the creation and deployment of value-added Internet services such as VoIP, video-on-demand, and other emerging QoS-sensitive services. A SON purchases bandwidth with certain QoS guarantees from individual network domains via a bilateral service level agreement (SLA) to build a logical end-to-end service delivery infrastructure on top of existing data transport networks. Via a service contract, users directly pay the SON provider for using the value-added services provided by the SON. We study the bandwidth provisioning problem for a service overlay network which is critical to the cost recovery in deploying and operating value-added services over the SON. We mathematically formulate the bandwidth provisioning problem, taking into account various factors such as SLA, service QoS, traffic demand distributions, and bandwidth costs. Analytical models and approximate solutions are developed for both static and dynamic bandwidth provisioning. Numerical studies are also performed to illustrate the properties of the proposed solutions and demonstrate the effect of traffic demand distributions and bandwidth costs on the bandwidth provisioning of a SON.