It is projected that hundreds of cores can be integrated into a chip at the sub-20nm technology nodes. However, some challenges exist in the many-core architecture such as maintaining memory coherence, underutilized parallelism, and increased inter-core communication delay. This work proposes the data-center-on-a-chip (DCoC) paradigm employing virtualization technologies commonly used in today's data centers to reduce the overhead of maintaining memory coherence and inter-core communication and improve parallelism. In the DCoC paradigm, user applications with specific resource requirements need to be mapped onto different chips of a data center and different cores of a chip in the form of virtual machines (VMs). By a judicious VM mapping method, the data center performance can be maximized while satisfying the power budget and power density constraints of the chips and the resource requirements of VMs. To tackle the NP-hardness of the VM mapping problem, we propose a two-tier algorithm, which effectively solves the mapping problem with polynomial time complexity.