I have this melody in the book of 'Traditional Slow Airs of Ireland,' edited by Tomas O Canainn.

He calls it Gol na mBan san Ar.

It is true that the word 'children' makes more sense than 'chill' but that's only if you think the song is addressed to children. I think it's addressed to birds.

How could children go west to Ardmore and east to Tramhor when they go to sleep?