This post refers to Squarespace 6 and the answer is now outdated. For help adding a video to a Gallery Page in Squarespace 7, please check this guide: https://support.squarespace.com/hc/en-us/articles/208404698-Adding-images-and-videos-to-a-Gallery-Page
Answer by jasonbarone · Jan 30, 2013 at 10:14 PM
Squarespace Gallery Blocks now support videos. Create a new gallery, add your videos (or just one video), set the Gallery to "grid" design, and select "lightbox".
Use this method to create single videos, or "thumbnail strips" of videos.
Video Demonstration: http://youtu.be/AOZdYsI46NE
Credit to @foleyatwork for bringing this to my attention.