An Italian media outlet reported last night that Enrico Mosetti (28) and two British colleagues, Ben Briggs and Tom Grant, had achieved the feat.
The face was the last on the mountain to be climbed (1970), and is still scaled only rarely.
Mosetti made his name with a 2015 solo expedition in Peru. On a 2016 Pakistan expedition one of his three Italian colleague was killed.
Skiing down the treacherous, avalanche-swept Caroline Face of Aoraki-Mt Cook has been a goal for some of the world's most highly-skilled extreme skiers for several years.
Mountaineer Graeme Dingle, who was in the second pair to climb the Caroline in 1970, after four deaths on the route in the 1960s, has said the face would be skied eventually, although it would be extremely dangerous.
``It's right up there. You make one blue, catch an edge or hit a lump of ice and you're gone and you're not going to recover.''
The first ski descent of Aoraki/Mt Cook was by Wanaka climbing guide Geoff Wayatt, in 1982.
