The Ancient Greek Septuagint translation “high heaven” or “the heights” (רמים) as “unicorns” or “wild oxen” (ראמים), monokeroton (μονοκερώτων) in Greek. Translations that are based on the Septuagint, including Orthodox versions of the Psalter, do therefore use “unicorn” in this verse.

Examples include

• The English Psalter of the Prophet and King David according to the Septuagint (Michael Asser 2005 ) for the use of the Orthodox church: “And He built His sanctuary like that of an unicorn; He established it upon the earth for ever.”
• The English Septuagint translation by Nicholas King, SJ (2013): “He built his sanctuary like the place of unicorns; he founded it on the earth forever.”
• The Finnish Ortodoksinen Liturginen Psalttari (2021): “And he built his sanctuary like that of the unicorns (yksisarvisille), establishing it on the earth for all time.”

Seppo Sipilä (in: The Bible Translator 2007, p. 171ff. ) comments on the choice between “unicorn” and “wild ox”: “Since the question is about the temple of the Lord, using any natural animal could be problematic in this psalm. In particular the suggestion that in (some) psalms the animal in question could be a wild ox is potentially dangerous, because the OT writers hesitate to use the ox as a symbol for the Lord.”

See also wild ox (unicorn).