From the Christian Science Monitor (link):
The Luding Bridge battle is the most famous moment in the Long March, itself the defining legend of modern China. The Red Army is hotly pursued in 1935. Soldiers hoof it 24/7 for 140 miles. They must cross the Dadu River, or be wiped out! But a 300-year-old chain-suspension bridge is closely guarded. So a suicide squad shimmies over the chains, under machine-gun fire, and wipes out the dreaded Nationalist enemy. The Red Army crosses! The China of Mao is saved!
Mao told the story to American chronicler Edgar Snow, who apotheosized it in his 1937 “Red Star over China.” Mao’s poem about the battle, “Gunfire licked the heavens/ Iron chains rocked,” is included in the book and became a Chinese Gettysburg Address, memorized by kids.
Just one problem: A “battle” never quite happened.
Read also an official history of the Luding Bridge Battle, via China Daily (link):
Crossing the Luding Bridge
Next was the crossing of the Luding Bridge, about a 1,000 li to the north. A li is an interesting distance measurement. An uphill li is shorter than a downhill li. So, it measures how long the journey will take not how far. They had to beat Chiang to the river, and they did. Next was the race to the Luding bridge. It was an ancient structure built in 1701. This bridge is situated to the west of Luding County. The bridge measures about 100 meters long and 2.8 meters wide. Thirteen chains supported the side supports as well as those for the bridge floor. Irregular planking lay on the flooring. The bridge is still there today. They had 100 miles to get to the river in two days and then take the bridge. Abandoning their equipment except rifles and bullets, they raced to the bridge. On the other side of the river, a KMT unit was also racing to the bridge. The KMT unit stopped for the night and the Red Army beat them to the bridge. On May 29, 1935, the Red Army arrived here. Despite of the heavy gunfire from the enemy troops stationed at the bridge and the fact that the KMT had removed the planking, the Red Army assault team of 22 crawled forward, exterminated the enemy force and took the bridge with a loss of only 7 men.