Bruce played the song 2 times as a snippet:
during the DETROIT MEDLEY
1984-12-13 - MID-SOUTH COLISEUM, MEMPHIS
It is stated in the book Blinded by the Light that the set included a version of "Memphis, Tennessee" but it is not in evidence on the known tapes. It's likely that the Chuck Berry song was included in "Detroit Medley" (which did include "Travelin' Band"), as it was the following night in the same venue.
Bruce covered the song only once in Memphis during the "Detroit Medley" . The medly includes the first and last verses of Chuck Berry's "Memphis, Tennessee" towards the end.
Bruce on the artist
When Chuck Berry died Bruce tweeted :
"Chuck Berry was rock's greatest practitioner, guitarist, and the greatest pure rock 'n' roll writer who ever lived. This is a tremendous loss of a giant for the ages."
Springsteen and Berry played together on at least two occasions. As back up at the University of Maryland in 1973. Springsteen asked what songs they were going to do. Berry said : " we're going to do some Chuck Berry songs." More than 20 years later, Springsteen again played backup for Berry, at a concert at Cleveland Municipal Stadium,
celebrating the opening of the Rock and Roll Music Hall of Fame.
Bruce had 3 performances together with Chuck Berry:
1995-09-02 Cleveland Municipal Stadium, Cleveland, OH
The Rock And Roll Hall of Fame inauguration concert
1987-01-21 Waldorf-Astoria Hotel, New York City, NY
The second annual Rock And Roll Hall Of Fame ceremony.
1973-04-28 Cole Field House, University Of Maryland, College Park, MD
One show, triple bill, with Chuck Berry headlining, [Lee Lewis]] second billed and Bruce and the boys opening. A show now steeped in legend. Berry's contract stipulated that it was the promoter's responsibility to supply him with a backing band for this concert. Apparently Bruce learned about a week before the show that the promoter was seeking a group to support Berry and immediately volunteered his band's services for free, which the promoter gladly accepted. There was no rehearsal or soundcheck with Berry, so Bruce and the boys improvised as best they could. The show was Bruce's first known appearance in Maryland. Bruce and the boys opened their part of the show with a 50-minute set, followed by a 60-minute set by Jerry Lee Lewis and his band. Chuck Berry (with Springsteen's entire band backing him, including Bruce and Southside Johnny) closed the evening's festivities with a 70-minute performance. Springsteen recounts some hilarious details in the 1987 Chuck Berry documentary Hail! Hail! Rock 'n' Roll, but does not mention Southside Johnny’s appearance. Fearing that Berry might not want a harp player Bruce positioned Southside in the shadows at the extreme end of the stage. However Berry enjoyed the harp playing and near the end of the show he actually acknowledged Southside to the crowd saying "that white boy can blow, can’t he!" This almost sold out gig in the 15,000 seat Cole Field House was not without some controversy. Such was the demand to see the show that the school newspaper reported that twenty people were arrested when police spotted individuals sneaking into the concert via an open female lavatory window at the back of the building. Apparently 200-300 people made it in before the police caught wind of what was going on.
Watch Bruce tells the story here
List of songs co-credited to Bruce Springsteen and Chuck Berry: