Kirkjugólfið (The Church Floor) is in the field just east of Kirkjubæjarklaustur. It's an approx. 80 m² expanse of columnar basalt, eroded and shaped by glaciers and waves. There has never been a church there but the plane looks as though it's man made. Columnar basalt is formed when lava flow gets cooled and contraction forces build up. Cracks then form horizontally and the extensive fracture network that develops results in the six sided formation of the columns. Kirkjugólf is a protected natural monument.
Hildishaugur (Hildir's Mound), the mound of Hildir Eysteinsson lies a short way from Kirkjugólf. In Landnáma (The Book of Settlement), a medieval Icelandic manuscript, it is said that Ketill fíflski (Ketill the Foolish) lived at Kirkjubær, but Ketill was a Christian. Earlier, Irish hermits (Papar) lived at Kirkjubær and tradition says that the place was enchanted, so that pagans couldn't live there. Hildir Eysteinsson, a pagan, didn't believe this and attempted to move to Kirkjubær. When he set foot on the estate, he fell down dead.