Laman Damodred took the throne in 965 NE. Sometime prior to 978 NE, he chose to cut down the 500-year-old chora tree given to Cairhien by the Aiel to make a throne for himself. This act, often referred to as 'Laman's Pride' or 'Laman's Sin', brought great numbers of Aiel over the Spine of the World and precipitated the Aiel War. This ended with death of Laman, by then called Laman Treekiller, at the hands of the Aiel on Danu 1, 978 NE. Laman's brothers Moressin and Aldecain were also killed. Their goal complete, the Aiel returned to the Waste as suddenly as they came.
Even today, Aiel are distrusting of the Cairhienin, referring to them as "treekillers" and "oathbreakers". The feeling is quite mutual, considering the slaughter caused by the Aiel as they cut their way to King Laman.
The Aiel kept Laman's sword as a trophy. It was a very rich sword, with an ivory hilt, and a gold pommel encrusted with gemstones - a Power-wrought blade refitted for ostentation, not for combat. The sword itself would pass through several owners until decades later, when Aviendha acquired it and offered it to Rand al'Thor thinking to free herself of the toh she incurred when Rand innocently gave her a bracelet as a gift. Rand accepted the heron marked blade itself, but chose to let Aviendha keep the impractical and gaudy scabbard and hilt including all the gems.