Sigmundur Brestisson (961–1005) was a Faroese Viking chieftain, and was responsible for introducing Christianity to the Faroe Islands in 999.

Initially Sigmundur sought to convert the islanders by reading the decree to the Alting in Tórshavn, but was nearly killed by the resulting angry mob.

He then changed his tactics, went with armed men to the residence of the chieftain Tróndur í Gøtu and broke in his house by night.

Later, in 1005, Tróndur í Gøtu attacked Sigmundur by night at his yard in Skúvoy, whereupon he fled by swimming to Sandvík on Suðuroy.

He reached land in Sigmundargjógv in Sandvík, but a farmer in the village killed the exhausted Sigmundur, and stole his precious golden arm ring.