Chauvel called it Le Lanceur de Grenades, as it shows a French soldier throwing a grenade. But the players called it La Coupe de la Somme, (the Somme Cup).
Last week in Paris a team drawn from the New Zealand armed services, the Defence Blacks, played once more for the Somme Cup.
They beat a French Military Pacific XV 50-0, but there was no trophy to mark the occasion.
A Defence Force spokesman said searches of online collections of major New Zealand cultural institutions had failed to turn up a record of the cup, and its whereabouts seemed unknown.
"Inquiries as to the Somme Cup's location are ongoing and the NZDF are very interested in any information about it - not only as a significant military trophy but also as a key historical New Zealand sporting award."
The Defence Blacks play in Belgium this weekend in honour of a famous All Black - Dave Gallaher, captain of the Originals, the national side that toured Britain in 1905-06. Gallaher was fatally wounded on October 4, 1917, during the Passchendaele offensive.
He was among the 484 New Zealanders cut down in the battle for Broodseinde, which was seen as a "success" for the British-led forces.
The game is at Zonnebeke, a Belgian town near Tyne Cot cemetery.
The World War I cemetery includes the graves of 520 New Zealand soldiers, 322 of them unidentified.
A memorial wall at the rear of the 3.5ha cemetery commemorates 1176 New Zealanders who have no known grave and were casualties of conflict on the Western Front.
A service to honour the Broodseinde casualties is being held at the Zealand Battlefield Memorial's Graventafe.
Next week the New Zealanders head to Britain for the International Defence Force Rugby World Cup.