Born in 1975, Héðinn won the World U12 Chess Championship in 1987. The next year, he competed at the World U14 Championship, held in Romania. Ceaușescu was the still in power at the time and there was not enough food for the competitors; Héðinn suffered from malnutrition during the event and fell ill. In 1990, he won the Icelandic Chess Championship, aged 15. The same year, he competed at the 29th Chess Olympiad, scoring 1½/3 as Iceland finished eighth out of 108 teams. At this time, his Elo rating was over 2500. He earned his international master title in 1994 and his grandmaster title in 2007.