Kevin Costner’s Yellowstone official trailer released! Paramount Network has released the official trailer for Kevin Costner’s new series, Yellowstone, which follows the violent world of the Duttons, a ranching family in Montana, and is set to premiere on Wednesday, June 20 at 9:00 p.m. ET/PT. Check out the Yellowstone official trailer in the player below and let us know what you think! Two-time Academy Award winner Kevin Costner stars as John Dutton, the patriarch of the family who controls the largest contiguous ranch in the United States, under constant attack by those it borders – land developers, an Indian reservation, and America’s first National Park.