Years after that terrible night, which he spent huddling for shelter from the savage air raid and the firestorm that razed 75 per cent of Dresden and killed 35,000 people, Mr Eichner, now 80, found the chess piece - a knight. It was on the small patch of ground where he had endured the onslaught.
"It is the only thing I managed to salvage from the bombing and every time I look at it I am overcome by emotions I can't control," he confessed this week.
In February 1945, Mr Eichner had recently returned from the Russian front. The 20-year-old machine gunner was billeted at a military hospital in a converted school in Dippoldiswalde Street, about a mile from the city centre, and was recovering from his wounds. "My father and I were chess players," he recalled. "My father brought his chess set to the hospital to help me while away the time. When the bombing started, I just thought I must hang on to the chess set."
In the end, only the board was any use - for beating out the flames on his and his companions' heads and, when all their hair had burned, to put out the flames on their clothes and skin.
By Dresden standards, Mr Eichner was better equipped than most to cope with the raid. His hospital had a team of trained fire fighters and he and his wounded comrades survived the first wave of bombing almost unscathed.
Together, they extinguished scores of RAF incendiary bombs that had burned their way through the roof of the building. "We were ready to go on fighting the fires until it was all over," Mr Eichner recalled. But then, at around 1am on the morning of 14 February, came the second RAF raid.
"There were no warning sirens," he said. "We were completely surprised and rushed back down into the cellars of the hospital. But these quickly became hopelessly overcrowded with people who could no longer find shelter in their own burning buildings. The crush was unbearable, we were so tight you couldn't even fall over."
The hospital received several direct hits. The lights went out and bricks from the safety wall over the windows were blown into the basement. "The air was thick with dust and smoke that was choking us. I remember seeing one woman throw herself across her baby's cot in an attempt to protect her child," Mr Eichner recalled.
Then someone shouted that the ground floor of the hospital was on fire. "We had to get out but we had no idea where to go," Mr Eichner said. "Apart from the fire risk, it was becoming impossible to breathe in the cellar because the air was being pulled out by the increasing strength of the blaze."
He and five other soldiers emerged from the hospital basement into the growing firestorm that was sucking air at hurricane force towards what by now was the inferno of the old town. "We could not stand up, we were on all fours, crawling," Mr Eichner said. "The wind was full of sparks and carrying bits of blazing furniture, debris and burning bits of bodies."
The six men found a spot in a front garden behind a pile of rubble and made a circle. "Our faces were covered in wet rags and we spent the next six hours beating out the fires that kept flaring up in our hair and on our clothes that were tinder dry. We just kept praying," he recalled.
By now the asphalt surface on many of the streets had melted and was tearing the shoes off Dresdeners who were fleeing the cellars of their burning homes. Many of the victims who suffered badly burned feet could not go on. They slumped to the ground and choked to death on the fumes.
Hundreds of others sought safety in large concrete reservoirs that had been built in the town centre a year earlier to help fire-fighters. However, these proved a treacherous refuge because the smooth-sided tanks were more than 10 feet deep and had no ladders. By daylight, many inside had drowned.
But, as the light of dawn became dimly visible through the smoke, Mr Eichner and his five companions knew they had survived the worst. They could hardly see - their eyes were swollen red from the smoke, and their skins were like parchment but covered in weeping blisters. They had all lost their hair, eyelashes and eyebrows.
Mr Eichner made his way towards the main railway station which had been packed with refugees at the time of the raid. He saw terrible scenes. "There were charred bodies everywhere," he said. The corpses were blackened around the torsos but the legs were "pink like pork". There at the station, Mr Eichner found his father. He had collapsed with exhaustion after spending hours shifting corpses. The two fell into each other's arms and made their way across the devastated city. They narrowly missed being crushed by the falling facade of a burned-out building.
In the days that followed, Mr Eichner remembers crossing the Altmarkt, the old town square, when SS guards - sent from a Nazi death camp - were supervising the burning of 6,865 bodies piled in a heap. The operation took two weeks to complete. Today, Mr Eichner will unveil a plaque on the Altmarkt in memory of the dead.
"The experience of the bombing was far worse than being on the Russian front, where I was a front-line machine-gunner before I was wounded," Mr Eichner said. "At the front, you were scared most of the time, but at least you had some freedom of action. During the firestorm, the worst thing was that you felt completely powerless. You could do nothing but wait and pray."
Despite the horror of his experiences that night, he doesn't blame the British: "No, like me, they were just fighting a war and trying to end it as quickly as possible."
As we walked through Dresden this week, Mr Eichner pointed to the city's granite paving stones - among the only original features to survive the firestorm and subsequent reconstruction. Nearly every stone is deeply scored by shrapnel splinters from the raid.
In photographs he took of Dresden in the early 1950s, the city centre is like a great moonscape - just three buildings marginally intact in an ocean of rubble. "Around here the houses were built so closely together that you could shake hands across the street from your bedroom window," he recalled as we crossed an area that is now a soulless, concrete arcade.
Despite the rebuilt Frauen-kirche - the main structure was completed last June - and the painstakingly restored Baroque buildings of the old town, once immortalised by Canaletto, Dresden is still a city with too many green empty spaces to feel at ease.
"For me, most of Dresden is an open wound," Mr Eichner remarked. It was hard to disagree.