The Studio master of "Blue Christmas" was recorded by Elvis during the first of a three day recording session at Radio Recorders in Hollywood, California on 5 September 1957.
The sessions were intended to yield tracks for Elvis' first Christmas album and all but two of the eleven tracks cut over the three days were of the seasonal variety. The nine Christmas songs complemented by three gospel tracks recorded in January of the same year and a classic Elvis album was born.
"Blue Christmas" was the second of only two songs recorded that first day with the other being "Treat Me Nice".
Of the Christmas songs on that first album, and indeed of subsequent recordings, "Blue Christmas" has probably become the most enduring and well known. It is more often than not the Elvis track included on mainstream Christmas compilations.
On stage in the 70's Elvis sang "Blue Christmas" more than fifty times and it didn't seem to matter what time of year it was he still sang it. In one instance in Kansas City on 29 June 1974 he even sings the line 'You'll be doin' alright, with your Christmas in July!!".
The first time that Elvis sang in stage however, it was a bit closer to Christmas performed as it was on 16 November 1970 during the penultimate show of Elvis' second full tour after his return to the stage,
It seems unrehearsed and if this is indeed the case the band seem to catch on quickly with a little guidance from Elvis and it is a nice version.
https://www.youtube.com/watch?v=7YqWPs1gCyQ