"Eutopia" is a short story by American writer Poul Anderson that originally appeared in Harlan Ellison's 1967 science fiction anthology Dangerous Visions.
In that timeline, Christian Western Europe was overwhelmed in the tenth century by the combined onslaught of the Scandinavian Vikings from the north, the Magyars from the east and the Arabs from the south.
Afterwards, the Arab Caliphate disintegrated in internal discord while the Vikings and Magyars, who kept their original religions, dominated Europe and eventually colonized North America.
This North America, divided into numerous independent principalities, is much more sparsely populated than in our world, with large tracts of virtually untouched nature.
However, the vow is unbreakable, and Iason receives transport to where he could finally get to back to his home universe – the self-styled "Eutopia" which gives the story its name, an Earth where classical Greece came to dominate the planet.