From
http://www.borgarfjordur.com/pages/enpage2.html:
At Borg á Mýrum lived the settler Skallagrímur Kveldúlfsson. Skallagrímur is known as the third settler in Iceland. Most of the district of Borgarfjörður is said to have been his property. Skallagrímur established many farms where the farmland was best. Snorri Sturluson lived at Borg for a while before he moved to Reykholt. At Borg a church has been officiated since 1002, said to be one of the oldest church sites in the west of Iceland. The present church was built 1880. At Borg there is the monument Sonatorrek (Lament for my sons) by smundur Sveinsson.