Chon-kar is a Narn blood oath, or vow of vengeance.
In Narn culture, when a Chon-kar is declared the head of the family is honour bound to see it through and in the event that they are killed the responsibility falls to the next in line. Na'Toth's family had sworn a blood oath against the Dilgar war criminal Jha'dur. Na'Toth's grandfather and his family were on Hilak VII when the Dilgar invaded. Jha'dur used them in her illegal medical experiments, killing all but Na'Toth's grandfather who escaped back to Narn, but not before Jha'dur implanted a cybernetic device in his brain that would slowly kill his mind and spirit, leaving his surviving family helpless to do anything but watch.  A Narn family declared a blood oath against House Drusella during the Second Centauri Occupation of Narn.