The Brygjafael clan goes to Groenholt to enjoy the hospitality of Vigfus the Proud about a week prior to the Althing. Brygjafael plans to send a longship up the Hudson River and hopes to gather 5 ships total for the expedition. Vigfus promises to fund and send another longship. He has ties with Aestein of Raudarbank, and suggests them as possible expedition partners. They may try to boss everything and take the credit, though. Poul of Brygjafael is not at this gathering - he is off gathering witnesses among the Lagakin for their case at the Althing.
During dinner at Groenholt, Borgny the Sharp-tongued's daughter Vagnhild asks Kjartan to tell the story of "Grim the Truthful". Many are eager to hear a nasty satire, but Kjartan convincingly tells the tale of Thorfinn's effort to prove his parents which portrays the insult to Grim as a misunderstanding. However, under pressure for a more exciting tale, Kjartan then tells the tale of the Headless Horseman. Skallagrim drinks heavily and in a mood of black despair, makes cryptic references to some doom which haunts him. He also flirts with Borgny the Sharp-tongued and it is clear to all that he admires her.
Also at the feast, Vagnhild rather sullenly recites a poem about a hero who is overshadowed by many cousins. Thorfinn is much admired by Vigfus the Proud's eight granddaughters.
During the Althing, Thorfinn decides to pay his respects to his mother's family among the Tjaraholt clan. He is nervous and asks Kjartan to come along. At the Tjaraholt tent, no one comes to welcome them. They hear a couple inside fighting - a wife seems to be accusing her husband of infidelity, there is a loud slap, and Steingest the Goodlooking storms out complaining that the women of his family never listen.
Inside, Thorfinn introduces himself and states his purpose, to pay his respects to his maternal grandmother, Herdis the Old. The cousins are greeted by Ingrid the Wise, Thorfinn's aunt. Alfdis asks Kjartan to stand witness in her divorce case against Steingest (who just slapped her). Kjartan agrees that he will say what he heard and saw. Thorfinn is taken off alone to talk with Herdis, who gives him a hard time about his proper place in the family, and she refers to Thorfinn's fine horse - his mother's - that she sees with them. This goes over Thorfinn's head completely.
Meanwhile Bront has come into the tent and accosted Kjartan. They go into a corner and talk. Bront suggests that his son Brom is a good man, young and hotheaded, and it would be a shame if he were to be talked about badly.... Kjartan feels a heady rush of power as he realizes that Bront is worried about Brom becoming the subject of poetic satire and thus public gossip. He tells Bront about the longship expedition and suggests that Brom would have a chance in it to win glory in battle and direct his energies to something useful. It is likely that this conversation was overheard by most of the women of Tjaraholt.
During the Althing Skallagrim talks up the expedition and sizes up likely young men who might go, watching the contests in swordplay and archery. He gives much valuable advice to the Brygjafel family in several situations; he is a man of few words (unless drunk) but what he says is eminently sensible. He knows how to conduct raids and fit out a ship for a war campaign, and he also knows how not to do it - he keeps telling us how bad his former warlord was. (His former warlord was the Earl of Hvalrik?)
Poul states his case before the Althing, that the Tjaraholt clan owes weregeld to the Tappan Lagakin, from when Killer-Gest killed eight of their tribe. Unfortunately some of the witnesses don't show up, which weakens the case. Still, 40 cows of weregeld is awarded to the Tappans. Poul explains to them that it probably should have been higher.
Kjartan and Brom fight their holmgang, a duel in a sort of boxing ring set up in the middle of a ford. When blood drips onto the cloth floor of the ring, the duel is supposed to end. Also, whoever steps outside of the ring loses, and if both feet leave the ring, it's considered very dishonorable, as if the loser were a coward and were running away.
In the ring, Kjartan taunts Brom with being a beardless boy. The drunken crowd quaffs ale and laughs uproariously... Brom charges in a blind fury; Kjartan slips aside and wounds Brom in the leg. Brom's headlong rush carries him outside the ring into the water up to his knees! Skallagrim comments on how noble it was of Brom to leave the ring quickly after first blood was drawn. It is obvious that he's being sarcastic! Kjartan repeats Skallagrim's comment but in a more convincing way. Fortunatly Brom does not completely lose it -- at least not right now. There is mutual manly butt-patting and congratulations and mead-quaffing all around in the Brygjafael camp.