The Enterprise is commandeered by aliens who exist in a hyperaccelerated time frame.
Air Date: 11/01/68
Director: Jud Taylor
I always used to mix this episode up with "Wink of an Eye". Thankfully, reviewing the episodes as I have helped me to sort them out. This one is a classic Trek episode: enemy takes over ship, crew in peril, Kirk kicks butt. Some things never get old.