"It has always been a dream of mine, both as a little girl and as a performer," Hill said in an e-mail of the performance, which was taped for an installment of the Public Broadcasting Service's popular "Soundstage" series.
Hill taped the show, an exclusive performance of her new "Joy to the World" CD, this fall at the Sears Centre Arena in Chicago before an audience of about 3,000.
PBS will begin airing the program Thanksgiving week and repeat it through December.
During the show, Hill sings "Winter Wonderland," "O Come, All Ye Faithful," "What Child Is This?" and other songs from her new CD against a festive winter backdrop.
"It was really important to me to marry the music on the album, the way it was performed on the album, with the presentation of the stage," she said.
Hill, 41, said she drew from Christmas records by Burl Ives, Nat King Cole and Elvis Presley to get the sound she wanted.
"That period of Christmas music evokes thoughts of the season for me no matter what time of year that I hear it. It just strikes a chord with me."