Mitigating cybersickness can improve the usability of virtual reality (VR) and increase its adoption. The most widely used technique, dynamic field-of-view (FOV) restriction, mitigates cybersickness by blacking out the peripheral region of the user's FOV. However, this approach reduces the visibility of the virtual environment. We propose peripheral teleportation, a novel technique that creates a rest frame (RF) in the user's peripheral vision using content rendered from the current virtual environment. Specifically, the peripheral region is rendered by a pair of RF cameras whose transforms are updated by the user's physical motion. We apply alternating teleportations during translations, or snap turns during rotations, to the RF cameras to keep them close to the current viewpoint transformation. Consequently, the optical flow generated by RF cameras matches the user's physical motion, creating a stable peripheral view. In a between-subjects study (N=90), we compared peripheral teleportation with a traditional black FOV restrictor and an unrestricted control condition. The results showed that peripheral teleportation significantly reduced discomfort and enabled participants to stay immersed in the virtual environment for a longer duration of time. Overall, these findings suggest that peripheral teleportation is a promising technique that VR practitioners may consider adding to their cybersickness mitigation toolset.