It was called the Scotch Whisky Cup back then and it was his fourth final appearance in five years, yet it was another 24 years before Scotland won again, by which time Hay's sons, David and Mike, were both on the team, the latter as reserve.
Mike was just three years old when his father triumphed and rarely can there have been such an impact of nurture in sport. He won the first of five European titles at 18, and played in two world finals. He coached Rhona Martin (now Howie) to Olympic gold in 2002 and is the British Olympic Association's chef de mission at the Winter Olympics which open in Sochi next week. Rhona is Britain's head curling coach and Hay's brother, David, is also there, released from the family farm near Bridge of Earn. Chuck, now an octogenarian, keeps his eye on things while David coaches Eve Muirhead's world champion rink.
"Fundamentally, I am where I am now because of dad," says Mike. "He'd like the idea that it all kicked off with his rink of Perth farmers."
Yet the route was tortuous. Mike worked in the timber trade in Glasgow and Vancouver, oil and gas distribution in British Columbia and Scotland before joining sportscotland as curling coach in 1998. After the Turin Olympics he moved to the BOA.
The buck in Sochi stops with him. An intimidating brief covers delivery to Russia of all equipment: every nut and bolt, plans for every eventuality, from security in the face of terrorism to human rights demonstrations. Containers were shipped to the Black Sea in December: 6000 items as diverse as home-from-home athlete packs including tea, coffee, kettles, and irons; spin bikes and performance centre equipment (stretching mats and medicine balls); physiotherapy equipment; computers, printers, copiers and surge protectors.
Items like bobsleighs are still in use on the World Cup circuit and will be flown in at the last minute. Planning and attention to fine detail make the difference between a personal best, podium finish, or not.
Hay is married to a Norwegian, Hanne Woods, who won 18 world and European championship medals, including two gold at each. They live in London, but Mike is currently in Adler, some 20 miles from Sochi, a palm tree-fringed resort on the shores of the Black Sea. It is the most improbable Winter Games venue ever, constructed almost from scratch at a cost of some £31bn, making London 2012 look positively frugal.
Hay is in charge of all planning and organisation. "We start off about five years before a Games, going on recces, meeting host organising committees, setting up a relationship, getting to know the environment and assessing the challenges. I went first in 2009, and have made seven or eight visits."
There are contingency plans for just about everything. "We run scenarios with team leaders, covering all eventualities, and have a situation management plan for the bigger issues. They are all covered in a four-year course."
With recent suicide attacks, including 31 fatalites within a few hours' drive, and draconian statements regarding demonstrations on homosexuality, the BOA can afford no complacency.
There is a 100-kilometre security zone around Sochi, and the BOA has plain-clothes security officers who will travel with athletes. Thus far, says Hay, nobody has expressed reservations about participating.
Each member of Team GB is required to sign a contract, but Hay is adamant these do not impact on competitors' rights. "We are not putting words in athletes' mouths," he says. "Anybody who goes to the Games has to abide by the Olympic Charter, or they won't be competing there. It's the same for anyone who travels abroad - you may not agree with the laws a country has, but you need to respect them. Yet our Olympic team has to reflect the values of the nation we come from. Freedom of speech and freedom of expression is very dear to us, so we are trying to find a commonsense way of being able to do whatever we need to do, within that framework.
"We clarified between the hosts and Russian Government that there will be a protest zone outside the Olympic environment.
"If any athletes come to us and want to make a protest - and we have not had any - the first thing we have to do is spell out that it has to be done within the framework, within the laws, and in the safe environment . . . we are not in the business of imposing impediments or restrictions on freedoms beyond the requirements of the charter."
UK Sport is looking for three medals. Hay acknowledges their investment confers a right to set targets. He is "delighted they have got confidence in the team which has a lot of strength in depth, but I think it's a big challenge. The last time we won three medals was 1936, so let's not run away with the challenge."
"There are 12 additional sports from Vancouver, and three or four offer a great opportunity, especially new sports such as freestyle, and the snowboard slope-style and ski half pipe. We have some world class athletes, so I think it is going to give a nice edge to the team - new guys and new disciplines, especially when they come from these, shall we say, 'street sports' which the IOC has taken a leap of faith in. "Some winter sports have pretty big world championships, but the profile of winter athletes is not as high as their summer colleagues.
"It's a massive opportunity, and if we have a great Games it would help profile. We're fighting for the same athletes to come into winter sport against traditional rugby and football. If the guys do well in Sochi, become role models and tell the story of how they got into their sport, we have an opportunity in this country with the snow domes and ice rinks. We don't need Alpine ranges for many of these guys at the development stage."
With 30 curling rinks to just one in England, Scotland has all 10 curlers and 18 competitors in the 58-strong Sochi contingent, plus a good number of the backroom team. Predictably, Scotland's sports minister and sportscotland trumpet that the nation is "punching above its weight". Yet good though it is, it's actually fewer than four years ago. There were 19 Scots in a team of 43 in Vancouver - a significantly higher percentage.
Hay is adamant that Sochi is outstanding, but acknowledges that three villages (one for endurance disciplines at 1500m; a higher one for skiers, sliders, jumpers, freestyle and snowboard; and a third on the coast for ice sport) will stretch UK resources. "Yet for me, Sochi is the best and most unique concept we have had at a Winter Games," he says. "Vancouver was a great Games, but it was a two-and-a-half hour, tough drive between Whistler and the city cluster in Vancouver.
"Here we are just 35 minutes in a train, and little longer by car or bus. The five coastal venues are no more than 150m apart, and five minutes' walk from the coastal village.
"Vancouver had fantastic facilities, but you could be an hour across the city, just going from speed skating to curling. Here the logistics are great for spectators. Watching Alpine by day and figure skating in the evening is absolutely do-able. The concept is good. Clearly they've spent a lot of money, all brand new facilities - superb for athletes. Accommodation is also superb. There's a lot of good news we are not hearing about."
It was a different era when Robin Nash and Tony Dixon won bobsleigh gold in 1964. They had to borrow a bolt from Italian rival Eugenio Monti. There are 67 support staff to take care of such minutiae in Sochi and look after the competitors.
Nash said he had no knowledge of "a sports psychologist, whatever that is. If things got tense we would retire to a bottle of whisky".