The only hill, in this parish, is Couthboanlaw, now by corruption, called Quothquanlaw.-- The late Dr McFarlane, so celebrated for his knowledge in antiquities, was of opinion, that this hill derives its name from these two Erse words, Couth boan, which in that language, signify a beautiful, or smooth hill: And indeed, it is one of the most beautiful little hills, that is to be seen in any country. It is about 600 feet above the level of the Clyde, and is green to the very top. On this hill, the common people, to this day, point out, with much fond admiration, WALLACE's chair, where he had his abode, and held conferences with his followers, before the battle of Biggar. The chair is a large rough stone, scooped in the middle.
From the Statistical Account of 1791-99, v2 p235 (Libberton and Quothquan, County of Lanark).
Geograph shows the hilltop in less than romantic style with its addition of a traffic cone. But hopefully if you find a common person they can still point out where the chair is. I do hope so.