Modern massively multiplayer online games (MMOGs) allow hundreds of thousands of players to interact with a large, dynamic virtual world. Implementing a scalable MMOG service is challenging because the system is subject to high workload variability, but nevertheless must always operate under very strict quality of service (QoS) requirements. Traditionally, MMOG services are implemented as large dedicated IT infrastructures with aggressive over-provisioning of resources in order to cope with the worst-case workload scenario. In this article we address the problem of building a large-scale, multitier MMOG service using resources provided by a Cloud computing infrastructure. The Cloud paradigm allows customers to request as many resources as they need using a pay-as-you-go model. We harness this paradigm by proposing a dynamic provisioning algorithm, which can resize the resource pool of a MMOG service to adapt to workload variability and maintain a response time below a given threshold. We use a queuing network performance model to quickly estimate the system response time for different configurations. The performance model is used within a greedy algorithm to compute the minimum number of servers to be allocated on each tier in order to satisfy the system response time constraint. Numerical experiments are used to validate the effectiveness of the proposed approach.