"Chestnut" is also known as "Dove's Figary".
The tune was first published in The English Dancing Master (1651) although it disappears after the 8th edition in 1690. It also was published in Daniel Wright's Complete Collection of Celebrated Country Dances (1740), where it appears as "Dove's Figary". Samuel Bayard (in his article "A Miscellany of Tune Notes," in Studies in Folklore) finds that it was long part of the Welsh harpers' repertoire under various titles, including "Hyd y Ffrwynen" (Length of the Rushes), "Y Vrwynen Las" (The Green Rush), and "Llanciau y Dyffryn" (The Lads of the Valley). He found it hard to determine whether the melody was originally Welsh or English, but noted that it has been in traditional Welsh repertoire for some time. No early song words survive with the exception of a West-English carol set to the tune.
Printings can be found in British Harmony (1781), Bingley's Sixty of the Most Admired Welsh Airs (c. 1803 or 1810), Parry's The Welsh Harper (1848) and Bennett's Alawon fy Ngwlad {Lays of My Land} (1896). This tune resembles "God Rest Ye Merry Gentlemen", especially the initial phrase.
It was recorded on Country Capers by The New York Renaissance Band.