Though Eliot judged his 1939 play about the return of Harry, Lord Monchensey, to his family home a failure, it is now regarded as his finest.
Eliot's estimation of his own work was based on comparisons with 1930s British drawing-room dramas. But director Adrian Noble makes wider connections: Shakespeare, Marlowe and the ancient Greeks, and modern writers such as Beckett, Pinter, Pirandello and Ionesco.
Noble praises the play's ability to occupy a naturalistic world but go "through the veil" into a world beyond. A script full of dualities - past and future - it gives the sense of a frontier between this world and another. The central characters know the exhilaration of living with excitement and danger.
In The Family Reunion, Harry claims to have killed his wife, but we cannot be sure whether he says this because he is mad or whether he is merely acting mad. Here is the link with Hamlet, says Noble. It may be Harry is toying with his family as Hamlet plays with Polonius. And Harry's relation with Mary, approaching 30 and attracted to him, echoes Hamlet's relationship with Ophelia.
Eliot doubtless drew on Shakespeare for the play's setting, the family home of Wishwood. Woods in Shakespeare are places of self-discovery where characters are refined and become stronger. Harry returns to Wishwood to undergo a progress represented in other Shakespearean settings - the Vienna stews of Measure For Measure or the nightmare of Agincourt for Henry V.
Eliot wrote of the realistic and the spiritual, a rare mix in modern drama, and the production needs to balance naturalism and abstraction. "If you put a complete naturalistic set on stage, the characters sound absurd," Noble says.
"Allow the words and actors to create the world and you have both one foot in the realistic world and one foot firmly beyond the veil."
Eliot's starting-point for the play's Chorus is the Eumenides, the final part of Aeschylus' ancient Greek trilogy Oresteia. Orestes is pursued by the Furies after killing his mother to avenge the murder of his father. These spirits turn into kindly Eumenides when Orestes is acquitted of her murder.
Governing the stage at the Swan is a huge window through which the Furies are seen before they burst into "our space". These spirits wear human dress. "Eliot saw them as contemporary," Noble says. "In their evening dress - which is right - we see our nightmares as reflections of our own age." And seen by Harry's sister Agatha and servant Downing, they cannot be dismissed as symbols of his neurosis.
Harry's sisters Violet and Ivy, and half-brothers Gerald and Charles become the Chorus. It's important that the production "creates a world where it is logical and acceptable when the Chorus speaks," Noble says. "They are not an add-on."
The choric element gives Violet and Gerald dignity. Normally they are superficial, even laughable people.
"If they did not say the Chorus lines they'd be trivial, stupid characters. They gain depth, status and majesty by saying the Chorus lines.
"Even the most inarticulate human being has depth and a soul."
At the Swan Theatre, Stratford-upon-Avon. In repertoire to October 7. Details and tickets: 01789 403403