Cadet Uhura attends a dinner at the captain's table with a bunch of senior staff and other officers during which she admits that though she beat out several thousand applicants for the job on Enterprise, she might not be "all that Star Fleet."
Meanwhile, a comet the Enterprise is observing is on course to destroy a nearby planet with a young, pre-warp culture and when they try to push it off course, they discover that it has some alien tech on it.
What follows is an away team (which includes Cadet Uhura on her first away misson) that goes to the comet and gets trapped by a force-field and has to learn to sing to a giant egg to get free. Meantime, the Enterprise is getting shook down by "shepherds" of the comet who think of the away team as a desecration.
And it all comes down to clever math and translations, fancy flying from Ortegas, sneaky-sneakiness from Spock, and nerves of pure steel from Captain Pike. Can they pull it off? Will they pull it off?! and will Uhura stay with Star Fleet?!
