There was a man named Kettle Hæing, son of Thorkel earl of Naumdale, and of Hrafnilda daughter of Kettle Hæing of Hrafnista. He was a man of wealth and renown; he had been a fast friend of Thorolf Kveldulf's son, and was his near kinsman. He had been out on that expedition when forces gathered in Halogaland with intent to join Thorolf, as has been written above. But when king Harold went south, and men knew of Thorolf's slaying, then they called a gathering.

Hæing took with him sixty men, and turned to Torgar. Hildirida's sons were there, and few men with them. He went up to the farm, and made an attack on them; and there fell Hildirida's sons, and most of those who were there; and Hæing and his company took all the wealth they could lay hands on. After that Hæing took two ships of burden, the largest he could get, and put on board all the wealth belonging to him that he could carry; his wife and children also he took, and all the men that had been with him in the late work. And when they were ready and the wind blew fair, they sailed out to sea. A man named Baug, Hæing's foster-brother, of good family and wealthy, steered the second ship.

A few winters before Ingjolf and Hjorleif had gone to settle in Iceland; their voyage was much talked about, and 'twas said there was good choice of land there. So Hæing sailed west over the sea to seek Iceland. And when they saw land, they were approaching it from the south. But because the wind was boisterous, and the surf ran high on the shore, and there was no haven, they sailed on westwards along the sandy coast. And when the wind began to abate, and the surf to calm down, there before them was a wide river-mouth. Up this river they steered their ships, and lay close to the eastern shore thereof. That river is now called Thjors-river; its stream was then much narrower and deeper that it is now. They unloaded their ships, then searched the land eastward of the river, bringing their cattle after them. Hæing remained for the first winter on the eastern bank of the outer Rang-river.

But in the spring he searched the land eastwards, and then took land between Thjors-river and Mark-fleet, from fell to firth, and made his home at Hofi by east Rang-river. Ingunn his wife bare a son in this spring after their first winter, and the boy was named Hrafn. And though the house there was pulled down, the place continued to be called Hrafn-toft.

Hæing gave Baug land in Fleet-lithe, down from Mark-river to the river outside Breidabolstead; and he dwelt at Lithe-end. To his shipmates Hæing gave land or sold it for a small price, and these first settlers are called land-takers. Hæing had sons Storolf, Herjolf, Helgi, Vestar; they all had land. Hrafn was Hæing's fifth son. He was the first law-man in Iceland; he dwelt at Hofi after his father, and was the most renowned of Hæing's sons.

Ketill hængr hét maðr, sonr Þorkels Naumdælajarls ok Hrafnhildar, dóttur Ketils hængs ór Hrafnistu. Hængr var göfugr maðr ok ágætr. Hann hafði verit inn mesti vinr Þórólfs Kveld-Úlfssonar ok frændi skyldr. Hann var þá í úthlaupi því, er liðsafnaðr var á Hálogalandi ok menn ætluðu til liðs við Þórólf, svá sem fyrr var ritat. En er Haraldr konungr fór norðan ok menn urðu þess varir, at Þórólfr var af lífi tekinn, þá rufu þeir safnaðinn. Hængr hafði með sér sex tigu manna, ok sneri hann til Torga, en þar váru fyrir Hildiríðarsynir ok höfðu fátt lið. En er Hængr kom á bæinn, veitti hann þeim atgöngu. Fellu þar Hildiríðarsynir ok þeir menn flestir, er þar váru fyrir, en þeir Hængr tóku fé allt, þat er þeir fengu.

Eftir þat tók Hængr knörru tvá, þá er hann fekk mesta, lét þar bera á út fé þat allt, er hann átti ok hann mátti með komast. Hann hafði með sér konu sína ok börn, svá þá menn alla, er at þeim verkum höfðu verit með honum. Baugr hét maðr, fóstbróðir Hængs, ættstórr maðr ok auðigr. Hann stýrði öðrum knerrinum. En er þeir váru búnir ok byr gaf, þá sigldu þeir í haf út.

Fám vetrum áðr höfðu þeir Ingólfr ok Hjörleifr farit at byggja Ísland, ok var mönnum þá alltíðrætt um þá ferð. Sögðu menn þar vera allgóða landkosti.

Hængr sigldi vestr í haf ok leitaði Íslands. En er þeir urðu við land varir, þá váru þeir fyrir sunnan at komnir. En fyrir því at veðr var hvasst, en brim á landit ok ekki hafnligt, þá sigldu þeir vestr um landit fyrir sandana. En er veðrit tók minnka ok lægja brim, þá varð fyrir þeim áróss mikill, ok heldu þeir þar skipunum upp í ána ok lögðu við it eystra land. Sú á heitir nú Þjórsá, fell þá miklu þröngra ok var djúpari en nú er. Þeir ruddu skipin, tóku þá ok könnuðu landit fyrir austan ána ok fluttu eftir sér búfé sitt. Var Hængr inn fyrsta vetr fyrir útan Rangá ina ytri. En um várit kannaði hann austr landit ok nam þá land milli Þjórsár ok Markarfljóts á milli fjalls ok fjöru ok byggði at Hofi við Rangá ina eystri.

Ingunn, kona hans, fæddi barn um várit, þá er þau höfðu þar verit inn fyrsta vetr, ok hét sveinn sá Hrafn. En er hús váru þar ofan tekin, þá var þar síðan kallat Hrafntóftir.

Hængr gaf Baugi land í Fljótshlíð ofan frá Merkiá til árinnar fyrir útan Breiðabólstað, ok bjó hann at Hlíðarenda, ok frá Baugi er komin mikil kynslóð í þeiri sveit. Hængr gaf land skipverjum sínum, en seldi sumum við litlu verði, ok eru þeir landnámamenn kallaðir.

Stórólfr hét sonr Hængs. Hann átti Hválinn ok Stórólfsvöll. Hans sonr var Ormr inn sterki. Herjólfr hét annarr sonr Hængs. Hann átti land í Fljótshlíð til móts við Baug ok út til Hválslækjar. Hann bjó undir Brekkum. Sonr hans hét Sumarliði, faðir Vetrliða skálds. Helgi var inn þriði sonr Hængs. Hann bjó á Velli ok átti land til Rangár it efra ok ofan til móts við bræðr sína. Vestarr hét inn fjórði sonr Hængs. Hann átti land fyrir austan Rangá, milli ok Þverár, ok inn neðra hlut Stórólfsvallar. Hann átti Móeiði, dóttur Hildis ór Hildisey. Þeira dóttir var Ásný, er átti Ófeigr grettir. Vestarr bjó at Móeiðarhváli. Hrafn var inn fimmti Hængs sonr. Hann var fyrstr lögsögumaðr á Íslandi. Hann bjó at Hofi eftir föður sinn. Þórlaug var dóttir Hrafns, er átti Jörundr goði. Þeira sonr var Valgarðr at Hofi. Hrafn var göfgastr sona Hængs.