Which Beatles song consists only of a chorus?

'Verse 1' consists of  the chorus from SPLHCB

Sgt. Pepper's Lonely Hearts Club Band opens with the title track that establishes the concept (a reunion concert for the eponymous group). Crowd noise blends the sound of orchestral  musicians tuning-up to create the illusion of a live performance. 

The song climaxes with the MC (McCartney) introducing 'the one and only Billy Shears' and the single chorus builds to a crescendo.

Concept

Arguably, the band reunion concept begins to fade at this point. Later Lennon would dismissively describe the album as 'a bunch of mainly Paul's songs'. This may be harsh but it was apparent during recording that the concept was not really sustained. 

The Beatles road manager, Neil Aspinall, pointed  out that the fictional band appeared to disappear after the opening track. He suggested that listener needed to be reminded of the live performance on side two.

The result was the penultimate track "Sgt. Pepper's Lonely Hearts Club Band (Reprise)".  This emerges out of the fadeout from Good Morning, Good Morning, the returning guitar riff blending with  the chicken noise.

Transition

"Sgt. Pepper's Lonely Hearts Club Band (Reprise)" is a conscious attempt to recreate the energy of a live performance.  All four Beatles sing in unison, with George Harrison playing lead guitar. The tempo increases and the brass disappears. leaving only the stage instruments they might have used at the Cavern.  

The band briefly return to being what  the French called , the Yeah-Yeahs  - a sound boiled down to a repeated chorus. This blast from their past fades away and A Day in the Life takes over. It is a moment of transition in the Beatles story in which the cheerful smiles of the red album are replaced by the sombre, unsmiling faces of the blue one.

The Beatles Digital Teaching Pack  (free to download)