It's one way to get the attention of your group: to announce on the first morning that the couloir into which you are about to ski has killed several people. Thankfully, that isn't what Stefan, our long-haired Swedish guide, tells us – at least not before we drop into Trifide 1, one of a series of infamous, 45-degree chutes that in places are barely wider than a ski is long.
When the funnel of hard snow drops below you towards giant shards of rock, it's enough to focus the mind to know that one slip would end it all without being reminded you're turning in the tracks of dead skiers.
Falling is good – it means you're trying – and it's while trying not to fall that, so often, knees are twisted and tibia are broken. But sometimes falling is not an option. "We go one by one: this is controlled skiing," Stefan says before dropping. Looking almost vertically down as Stefan descends, my edges grip the hard slope like steel fingernails. And then I go, my skis swinging left and right with each turn, while loosened snow sloughs past in a white cascade.
For me, the thrill of fall-and-die skiing outweighs the risks. The heart beats harder, the eyes open wider and, at the bottom of a run such as Trifide 1, as the lungs gasp for air, the sense of accomplishment is greater.
It's a sense I'm beginning to get used to in La Grave, a place whose deathly name is whispered on chairlifts and between bar stools all over the world by people who have heard it offers probably the best lift-served off-piste skiing on the planet.
Permanently in the shadow of the hulking Meije – a fearsome, 4,000m peak of razor ridges and windswept glaciers – La Grave sits in the Vallée de la Romanche, 40 minutes from the resort of Les Deux Alpes. The contrast with that place is marked. Deux Alpes has 50 lifts serving 100 pistes topped up by 200 snow cannons. The archetype of European resort skiing, its mountains are marshalled and manicured like tilted golf courses. At La Grave, there is one lift, a rickety téléphérique thrown up in the 1970s, and no pistes. Nor are there snow machines or markers or ropes above cliffs. Once you get off the gondola, almost 3,000 metres up, you're on your own.
"Usually, we adapt the mountain for skiing," Stefan says. "Here you have to adapt for the mountain."
Stefan, who's 45, is a former Chamonix ski bum who first followed those whispers to this corner of the Alps with a bunch of other Swedes back in the 1980s. His friend, Pelle Lang, spotted La Grave's potential as a cult destination and opened Skiers Lodge, one of only a handful of places to stay. Sure the farming village has grown since then (population today: 500), and its reputation has turned the place into a magnet for serious skiers from all over the world, but it remains brilliantly backwards and far removed from the high-speed quad homogeny that defines much of European skiing.
The village is tiny. Stefan, who recently moved up the valley to be nearer good schools for his young son, is back for a long weekend with Pure Powder, a new British outfit devoted to just the sort of skiing that La Grave offers. I'm staying at the Edelweiss, a comfortable hotel with a great bar (although don't expect to drink anywhere in La Grave much beyond 10pm), and an incongruous if not unappealing hot tub in the basement.
Sadly, pure powder is thin on the ground in early March. All the skiing here is north-facing, which means the Meije holds its snow well. Temperatures in the valley and the village can be freezer-like. But when we arrive from Grenoble airport, an easy 90-minute drive away, a fiendishly warm wind whips through La Grave.
The freak conditions leave Stefan scratching his head the next morning, but there is only one way up. At the top of the gondola, Stefan hands us our harnesses for the weekend. On a good day, you'd need them for abseiling, but the warm days and freezing nights mean the severest couloirs – the ones you need to rope into or out of, or both – have frozen to become unskiable ribbons of ice.
Up on the glacier, where we start with a gentle run before tackling the Trifides, the risks are more immediate. The ice here can creep up to a foot in a single day, cleaving hidden crevasses overnight even into tracked runs. A harness at least gives you a chance of being pulled out if you're swallowed whole. After Trifide comes Banane, so-called because of its shape, and Partout.
This area is Chancel, a natural playground of chutes and drops. "Doug used to say skiing here was like playing mini-golf," Stefan tells me. "Doug" was Doug Coombs, the American pioneer of free skiing and star of countless ski movies. "He used it for training."
Coombs was the master of the free-flowing, big-mountain style that reinvigorated a sport once seen as snowboarding's square uncle. He made La Grave his winter base, sharing his passion for the place with clients who signed up to his steep camps. One ski writer compared Coombs's fluid style to "a droplet of water trickling down a rough plaster wall". However, in 2006 he came unstuck on the treacherous Polichinelle couloir. He slipped and fell while trying to rescue a friend. Both were killed. One local guide said that it was "like Superman dying".
Despite high-profile accidents such as these, Stefan, Pelle and the handful of guides who call La Grave home baulk at its reputation as "death mountain". It demands respect and competence but offers hugely rewarding challenges even to strong intermediate skiers. What you mustn't do, ever, is ski without somebody who knows the mountain well – ideally a mountain guide.
On day two, our options are so limited that Stefan drives us out of the valley to Montgenèvre. This is a resort near the Italian border linked to the giant Milky Way ski area. It's no La Grave, but the unplanned return to resort skiing will at least offer perhaps the run of the trip. More optimistically than with the expectation of deep snow, I've picked up a pair of giant powder skis from the free Black Diamond test centre at the hotel. They look as if they would be happier in the wake of a speedboat. But after hiking up Rocher de l'Aigle, or Eagle Rock, the view of a perfect untracked pitch through larch trees lit by the sun causes my feet to twitch in their boots.
For a moment, I feel almost like a droplet of water as I descend at speed, slaloming through trees as my fat skis don't so much cut through as meld with the snow. It's an astonishing sensation, sadly not repeated back at La Grave, where we return for our final two days in what ought to be a freeskier's paradise.
Not that Stefan or any of the group is disappointed. If La Grave teaches you anything (other than how to ski couloirs) it's that you ski on its terms or pay the price. And as Stefan tells us on the last, breathless climb back up to the village on the final afternoon, there are a lifetime of lines here – so what's the rush?
The writer travelled to La Grave with Pure Powder (020-7736 8191; purepowder.com) which offers Big Mountain ski trips to La Grave for €1,495 (with 10 per cent off if you book before the end of the month) including half-board accommodation, transfers and six days of skiing with a guide. Flights, equipment rental, lunches and drinks are not included.