Some big established clubs had been forced to play in that opening round as the Clarets sat things out. They included Benfica, Ajax and Juventus as well as Reims who had been drawn against Luxembourg champions La Jeunesse D'Esch and had beaten them 11-1 on aggregate.
For Ajax and Juventus it hadn't been quite so good a start as they went out to Fredrikstad of Norway and Bulgarians CDNA Sofia respectively.
No dates had been set. Both Burnley and Reims had submitted dates to the organisers but the two clubs hadn't agreed and therefore negotiations were taking place. Dates in November were considered the most likely.
The French Champions were fourth in the league when the two clubs were paired, and were without their two great stars through injury - Raymond Kopa and Juste Fontaine. They believed both would be fully fit and ready for Burnley.
Unlike Burnley they weren't new to the competition having twice played in it previously, in seasons 1955/56 and 1958/59 when, on both occasions, they were beaten by Real Madrid in the final.
The club had no fewer than ten full internationals on their books and it was thought they would provide formidable opposition for Burnley who were enjoying European football for the first time.
Only one country could ever have two teams in the competition, the holders plus that country's champions. That, on this occasion, was Spain with Real Madrid and Barcelona and the two teams were paired against each other.
The full draw was:
Benfica v Újpesti Dózsa
AGF Aarhus v Fredrikstad
Rapid Vienna v Wismut Karl Marx Stadt
IFK Malmö v CDNA Sofia
Real Madrid v Barcelona
Spartak Hradec Králové v Panathinaikos
Burnley v Stade de Reims
Young Boys Berne v Hamburg