The recent trend of migrating legacy computer systems to a virtualized, cloud-based environment has expanded to real-time systems. Unfortunately, modern hypervisors have no mechanism in place to guarantee the real-time performance of applications running on virtual machines. Past solutions to this problem rely on either spatial or temporal resource partitioning, both of which under-utilize the processing capacity of the host system. Paravirtualized solutions in which the guest communicates its real-time needs have been proposed, but they cannot support legacy operating systems. This thesis demonstrates the shortcomings of resource partitioning using temporally-isolated servers, presents an alternative solution to the scheduling problem called the KairosVM Flattening Scheduling Algorithm, and provides an implementation of the algorithm based on Linux and KVM. The algorithm is analyzed theoretically and an exact schedulability test for the algorithm is derived. Simulations show that the algorithm can schedule more than 90% of all randomly generated tasksets with a utilization less than 0.95. In comparison to the state-of-the-art server based approach, the KairosVM Flattening Scheduling Algorithm is able to schedule more than 20 times more tasksets with utilization of 0.95. Experimental results demonstrate that the Linux-based implementation is able to match the deadline satisfaction ratio of a state-of-the-art server-based approach when the taskset is schedulable using the state-of-the-art approach. When tasksets are unschedulable, the implementation is able to increase the deadline satisfaction ratio of Vanilla KVM by up to 400%. Furthermore, unlike paravirtualized solutions, the implementation supports legacy systems through the use of introspection.