This work describes the design and subjective performance of Foveated High Efficiency Video Coding (FHEVC). Even though foveation has been widely used for various forms of compression since the early 1990s, we believe its use to improve HEVC is new. We consider the application of, possibly moving, foveated compression in this work and evaluate scenarios where it can be used to improve perceptual quality of videos under constrained transmission resources, e.g., bandwidth. A new method to reduce artifacts during remapping is also proposed. The preliminary implementation considers a single fovea only. Experiments summarizing user evaluations are presented to validate our implementation.