And the 77-year-old climber isn't done yet. Speaking at Hong Kong's Royal Geographical Society earlier this month, Bonington recounted his first triumphs in the Himalayas and the Alps.
In 1961, Bonington, then 27, left the army to devote his time to mountaineering. His first goal was 7,861-metre Mount Nuptse - next to Everest - in the Himalayas.
From afar, the mountain looks like a massive wall guarding Everest. At the time, Nuptse was one of the most challenging climbs in the region.
There were three routes to the summit: through the west, central and south ridges. The west ridge was too long, and the south was too difficult, no matter how capable the climbers were. The central ridge showed the greatest promise, Bonington - who was knighted in 1996 for his services to the sport - says.
For days, his team went tirelessly up and down the ridge, working out a path with ice axes and lines of rope. In the battleground of ice and rock, they skirted around craters, crawled across tunnels and hacked their way up ice slopes.
Climbing Nuptse proved to be drawn-out and trying. Members of the team were pushed to their limit. The higher they got, the harder it was to progress.
"The ridge seemed absolutely endless," Bonington says. "For a while, I thought our chances of success were pretty dim."
After a month of hard work, the climbers reached within 700 metres of the summit. They negotiated their way up a couloir - a steep narrow gulley - and picked their way across a horizontal ridge, which was like a knife's edge. And finally they were there - at the summit.
"When I poked my head over the top of that gulley, I was looking across the other side," Bonington recalls. "There stood the huge southwest face of Everest. The incredible vistas were beyond my imagination."
The cost of scaling the mountain ate up all his savings, but Bonington was undaunted. The same year he travelled to Chamonix on Mont Blanc in France, where he met three other climbers, including the late Briton Don Whillans.
The four of them set out to become the first climbers to reach the top of the 4,807m Central Pillar of Freney on the south side of Mont Blanc. It was "the last problem of the Alps", as Bonington puts it.
Just four weeks before, a French-Italian team got caught in a deadly storm. Four of the seven climbers died on the mountain.
To complicate matters, Bonington's team was being trailed by a team of three French climbers, who were also chasing the glory of reaching the summit first.
"They literally sent us running up the slopes," Bonington recalled.
In the final bid for the summit, they began to climb a steep rock face where they managed to lose their pursuers. The rock face was smooth with no handholds or cracks where you could place your feet for support. When Whillans' rope ran out half way, he became stuck, unable to get up or down.
"I remember Whillans call out, 'I'm coming off, Chris',", Bonington remembers, laughing. "Then a tangle of arms and legs came down from 20 metres above and he hung upside down spinning in mid-air."
They spent a whole day tackling the rock, managing to climb only 45 metres in the process. When finally they got to the top, they screamed and yelled with joy.
"Extreme climbing at high altitudes is very, very dangerous," says Bonington. "But I love everything about it: the physical business of climbing, the mountain environment, the company, and the exploring."
And he won't be quitting any time soon. "I'm excited by risk and want to keep doing it," he says.
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