Tryggvi "the Pretender" (Old Norse Tryggvi Ólafsson, Norwegian Tryggve Olavsson) was a Viking chieftain who lived in the early eleventh century, and came from "west across the sea" (probably from the Norse settlements in England and Ireland). His story appears in Heimskringla by Snorri Sturluson, the saga Morkinskinna, and a saga composed by Oddr Snorrason on Olaf Tryggvason.
According to Heimskringla, in 1033, during the lordship of Cnut the Great's son Svein over Norway, Tryggvi invaded Norway. He claimed to be the son of Olaf Tryggvason and his wife Gyda. His enemies scoffed at this claim, asserting that Tryggvi was instead the bastard son of a priest; however, Snorri Sturluson refers to Olaf's relatives in Viken as Tryggvi's "kinsmen;" moreover, the author of Morkinskinna has Harald Hardrada asserting kinship with the then-deceased Tryggvi, indicating that at least some people believed Tryggvi's claim.
When word reached Svein and his mother Ælfgifu of Northampton that Tryggvi's invasion was imminent, they summoned the landholders of Hålogaland and the Trondheim district to join the royal army in resisting Tryggvi. The jarl Einar Thambarskelfir, angered by the policies of Cnut's government, remained at home and refused to fight for Svein. Likewise, neither the powerful landowner Kálfr Árnason nor any of his brothers would fight for Svein.