St. Ambrose opens the ninth chapter of the first book of his treatise On the Holy Spirit with the following:
Now many have thought that the Holy Spirit is the ointment of Christ. And well it is said ointment, because He is called the oil of gladness, the joining together of many graces giving a sweet fragrance. But God the Almighty Father anointed Him the Prince of priests, Who was, not like others anointed in a type under the Law, but was both according to the Law anointed in the body, and in truth was full with the virtue of the Holy Spirit from the Father above the Law.
This is the oil of gladness, of which the prophet says: ‘God, even Thy God, hath anointed Thee with the oil of gladness above Thy fellows’ (Ps. 45(46):8. Lastly, Peter says that Jesus was anointed with the Spirit, as you read: ‘Ye know that word which went through all Judea beginning from Galilee after the baptism which John preached, even Jesus of Nazareth, how God anointed Him with the Holy Spirit’ (Acts 10:37, 38). The Holy Spirit is, then, the oil of gladness.
Both the word Messiah and the the Greek word Χριστóς (translated as Christ is English) mean Anointed One. As St. Ambrose points out, Christ — the Anointed One — is anointed with the Holy Spirit. It should come as no surprise, then, that Orthodox Christians should also be anointed with the Holy Spirit upon becoming members of the Body of Christ. Amen.